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Previous year question hub

Indefinite Integrals - Calculus - Mathematics Previous Year Questions

Practice Indefinite Integrals - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

87Papers
19Years
91Questions
1Topics

Indefinite Integrals question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Indefinite Integrals. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 72 79.1%
Hard 17 18.7%
Easy 2 2.2%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 77 84.6%
Numerical Answer Type (NAT) 14 15.4%

Subject weightage

Top subjects by unique question coverage.

Mathematics
91 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
91 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Indefinite Integrals
91 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Main 2026 (Online) 2nd April Evening Shift
1 Qs
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT
1 Qs
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT
1 Qs
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT
2 Qs
JEE Main 2021 (Online) 24th February Morning Shift
1 Qs
JEE Main 2021 (Online) 25th February Evening Shift
1 Qs
JEE Main 2021 (Online) 25th February Morning Shift
1 Qs
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT
1 Qs
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT
1 Qs
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT
2 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT
2 Qs
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT
1 Qs
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT
1 Qs
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT
1 Qs
JEE MAIN 2018 OFFLINE
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
1 Qs
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 OFFLINE
1 Qs
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2016 OFFLINE
1 Qs
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
1 Qs
JEE MAIN 2015 OFFLINE
1 Qs
JEE MAIN 2014 OFFLINE
1 Qs
JEE MAIN 2013 OFFLINE
1 Qs
AIEEE 2012
1 Qs
AIEEE 2008
1 Qs
AIEEE 2007
1 Qs
IIT-JEE 2007
1 Qs
AIEEE 2005
1 Qs
AIEEE 2004
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Evening Shift20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 29TH JANUARY MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 6TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Morning Shift20211View paper
JEE Main 2021 (Online) 25th February Evening Shift20211View paper
JEE Main 2021 (Online) 25th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20211View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT20202View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT20202View paper
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20191View paper
JEE MAIN 2018 OFFLINE20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT20181View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20181View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20181View paper
JEE MAIN 2017 OFFLINE20171View paper
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20171View paper
JEE MAIN 2016 OFFLINE20161View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20161View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20161View paper
JEE MAIN 2015 OFFLINE20151View paper
JEE MAIN 2014 OFFLINE20141View paper
JEE MAIN 2013 OFFLINE20131View paper
AIEEE 201220121View paper
AIEEE 200820081View paper
AIEEE 200720071View paper
IIT-JEE 200720071View paper
AIEEE 200520051View paper
AIEEE 200420042View paper

All Indefinite Integrals previous year questions

Practice every matching question in batches of 20, with every available option.

1
2004 · Mathematics · Calculus · Indefinite Integrals
AIEEE 2004
If \(\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,}\) then value of
\((A, B)\) is
A
\(\left( { - \cos \alpha ,\sin \alpha } \right)\)
B
\(\left( { \cos \alpha ,\sin \alpha } \right)\)
C
\(\left( { - \sin \alpha ,\cos \alpha } \right)\)
D
\(\left( { \sin \alpha ,\cos \alpha } \right)\)
Open complete paper
2
2004 · Mathematics · Calculus · Indefinite Integrals
AIEEE 2004
\(\int {{{dx} \over {\cos x - \sin x}}}\) is equal to
A
\({1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} + {{3\pi } \over 8}} \right)} \right| + C\)
B
\({1 \over {\sqrt 2 }}\log \left| {\cot \left( {{x \over 2}} \right)} \right| + C\)
C
\({1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} - {{3\pi } \over 8}} \right)} \right| + C\)
D
\({1 \over {\sqrt 2 }}\log \left| {\tan \left( {{x \over 2} - {\pi \over 8}} \right)} \right| + C\)
Open complete paper
3
2005 · Mathematics · Calculus · Indefinite Integrals
AIEEE 2005
\(\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx}\) is equal to
A
\({{\log x} \over {{{\left( {\log x} \right)}^2} + 1}} + C\)
B
\({x \over {{x^2} + 1}} + C\)
C
\({{x{e^x}} \over {1 + {x^2}}} + C\)
D
\({x \over {{{\left( {\log x} \right)}^2} + 1}} + C\)
Open complete paper
4
2007 · Mathematics · Calculus · Indefinite Integrals
AIEEE 2007
\(\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}}\) equals
A
\(\log \,\tan \,\left( {{x \over 2} + {\pi \over {12}}} \right) + C\)
B
\(\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C\)
C
\({1 \over 2}\,\log \,\tan \,\left( {{x \over 2} + {\pi \over {12}}} \right) + C\)
D
\({1 \over 2}\,\log \,\tan \,\left( {{x \over 2} - {\pi \over {12}}} \right) + C\)
Open complete paper
5
2008 · Mathematics · Calculus · Indefinite Integrals
AIEEE 2008
The value of \(\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}}\) is
A
\(x + \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c\)
B
\(x - \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c\)
C
\(x + \log \,\left| {\,\sin \left( {x - {\pi \over 4}} \right)\,} \right| + c\)
D
\(x - \log \,\left| {\,\cos \left( {x - {\pi \over 4}} \right)\,} \right| + c\)
Open complete paper
6
2012 · Mathematics · Calculus · Indefinite Integrals
AIEEE 2012
If the \(\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,}\) then \(a\) is
equal to :
A
\(-1\)
B
\(-2\)
C
\(1\)
D
\(2\)
Open complete paper
7
2013 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2013 OFFLINE
If \(\int {f\left( x \right)dx = \psi \left( x \right),}\) then \(\int {{x^5}f\left( {{x^3}} \right)dx}\) is equal to
A
\({1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} } \right] + C\)
B
\({1 \over 3}{x^3}\psi \left( {{x^3}} \right) - 3\int {{x^3}\psi \left( {{x^3}} \right)dx} + C\)
C
\({1 \over 3}{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} + C\)
D
\({1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C\)
Open complete paper
8
2014 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2014 OFFLINE
The integral \(\int {\left( {1 + x - {1 \over x}} \right){e^{x + {1 \over x}}}dx}\) is equal to
A
JEE Main 2014 (Offline) Mathematics - Indefinite Integrals Question 83 English Option 1
B
JEE Main 2014 (Offline) Mathematics - Indefinite Integrals Question 83 English Option 2
C
JEE Main 2014 (Offline) Mathematics - Indefinite Integrals Question 83 English Option 3
D
JEE Main 2014 (Offline) Mathematics - Indefinite Integrals Question 83 English Option 4
Open complete paper
9
2015 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2015 OFFLINE
The integral \(\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}}\) equals :
A
\(- {\left( {{x^4} + 1} \right)^{{1 \over 4}}} + c\)
B
\(- {\left( {{{{x^4} + 1} \over {{x^4}}}} \right)^{{1 \over 4}}} + c\)
C
\({\left( {{{{x^4} + 1} \over {{x^4}}}} \right)^{{1 \over 4}}} + c\)
D
\({\left( {{x^4} + 1} \right)^{{1 \over 4}}} + c\)
Open complete paper
10
2016 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2016 OFFLINE
The integral \(\int {{{2{x^{12}} + 5{x^9}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}} dx\) is equal to :
A
\({{{x^5}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C\)
B
\({{ - {x^{10}}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C\)
C
\({{{-x^5}} \over {{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C\)
D
\({{ {x^{10}}} \over {2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + C\)
Open complete paper
11
2016 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT
The integral \(\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}}\) is equal to :

(where C is a constant of integration.)
A
\(- 2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C\)
B
\(- 2\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C\)
C
\(- \sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}} + C\)
D
\(2\sqrt {{{1 + \sqrt x } \over {1 - \sqrt x }}} + C\)
Open complete paper
12
2016 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT
If   \(\int {{{dx} \over {{{\cos }^3}x\sqrt {2\sin 2x} }}} = {\left( {\tan x} \right)^A} + C{\left( {\tan x} \right)^B} + k,\)

where k is a constant of integration, then A + B +C equals :
A
\({{21} \over 5}\)
B
\({{16} \over 5}\)
C
\({{7} \over 10}\)
D
\({{27} \over 10}\)
Open complete paper
13
2017 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2017 OFFLINE
Let \({I_n} = \int {{{\tan }^n}x\,dx} ,\,\left( {n > 1} \right).\)

If \({I_4} + {I_6}\) = \(a{\tan ^5}x + b{x^5} + C\), where C is a constant of integration,

then the ordered pair \(\left( {a,b} \right)\) is equal to
A
\(\left( {{1 \over 5},0} \right)\)
B
\(\left( {{1 \over 5}, - 1} \right)\)
C
\(\left( { - {1 \over 5},0} \right)\)
D
\(\left( { - {1 \over 5},1} \right)\)
Open complete paper
14
2017 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT
The integral

$$\int {\sqrt {1 + 2\cot x(\cos ecx + \cot x)\,} \,\,dx}$$

\(\left( {0 < x < {\pi \over 2}} \right)\) is equal to :

(where C is a constant of integration)
A
4 log(sin \({x \over 2}\) ) + C
B
2 log(sin \({x \over 2}\) ) + C
C
2 log(cos \({x \over 2}\) ) + C
D
4 log(cos \({x \over 2}\)) + C
Open complete paper
15
2017 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT
If \(\,\,\,\) f\(\left( {{{3x - 4} \over {3x + 4}}} \right)\) = x + 2, x \(\ne\) \(-\) \({4 \over 3}\), and

\(\int {}\)f(x) dx = A log\(\left| {} \right.\)1 \(-\) x \(\left| {} \right.\) + Bx + C,

then the ordered pair (A, B) is equal to :

(where C is a constant of integration)
A
\(\left( {{8 \over 3},{2 \over 3}} \right)\)
B
\(\left( { - {8 \over 3},{2 \over 3}} \right)\)
C
\(\left( { - {8 \over 3}, - {2 \over 3}} \right)\)
D
\(\left( { {8 \over 3}, - {2 \over 3}} \right)\)
Open complete paper
16
2018 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2018 OFFLINE
The integral

$$\int {{{{{\sin }^2}x{{\cos }^2}x} \over {{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}} dx$$

is equal to
A
\({{ - 1} \over {1 + {{\cot }^3}x}} + C\)
B
\({1 \over {3\left( {1 + {{\tan }^3}x} \right)}} + C\)
C
\({{ - 1} \over {3\left( {1 + {{\tan }^3}x} \right)}} + C\)
D
\({1 \over {1 + {{\cot }^3}x}} + C\)
Open complete paper
17
2018 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
If    \(\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}\left( {{{x + 3} \over 4}} \right) + C\)
(where C is a constant of integration), then the ordered pair (A, B) is equal to :
A
(2,  1)
B
(\(-\) 2,   \(-\)1)
C
(\(-\) 2,  1)
D
(2,   \(-\)1)
Open complete paper
18
2018 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT
If \(f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,\) (x \(\in\) R \(-\){1, \(-\) 2}), then \(\int f \left( x \right)dx\) is equal to :
(where C is a constant of integration)
A
12 loge | 1 \(-\) x | + 3x + C
B
\(-\) 12 loge | 1 \(-\) x | \(-\) 3x + C
C
12 loge | 1 \(-\) x | \(-\) 3x + C
D
\(-\) 12 loge | 1 \(-\) x | + 3x + C
Open complete paper
19
2018 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT
If \(\int {{{\tan x} \over {1 + \tan x + {{\tan }^2}x}}dx = x - {K \over {\sqrt A }}{{\tan }^{ - 1}}}\) \(\left( {{{K\,\tan x + 1} \over {\sqrt A }}} \right) + C,(C\,\,\) is a constant of integration) then the ordered pair (K, A) is equal to :
A
(2, 1)
B
(\(-\)2, 3)
C
(2, 3)
D
(\(-\)2, 1)
Open complete paper
20
2019 · Mathematics · Calculus · Indefinite Integrals
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT
If \(\int {{x^5}} {e^{ - {x^2}}}dx = g\left( x \right){e^{ - {x^2}}} + c\), where c is a constant of integration, then \(g\)(–1) is equal to :
A
1
B
- 1
C
\(- {5 \over 2}\)
D
\(- {1 \over 2}\)
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