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Previous year question hub

Indefinite Integration - Calculus - Mathematics Previous Year Questions

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

9Papers
9Years
26Questions
1Topics

Indefinite Integration question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 26 100%

Question type distribution

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

Multiple Choices 26 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
26 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
26 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Indefinite Integration
26 Qs

Paper coverage

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

KCET 2025
2 Qs
KCET 2024
3 Qs
KCET 2023
3 Qs
KCET 2022
2 Qs
KCET 2021
4 Qs
KCET 2020
3 Qs
KCET 2019
3 Qs
KCET 2018
3 Qs
KCET 2017
3 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
KCET 202520252View paper
KCET 202420243View paper
KCET 202320233View paper
KCET 202220222View paper
KCET 202120214View paper
KCET 202020203View paper
KCET 201920193View paper
KCET 201820183View paper
KCET 201720173View paper

All Indefinite Integration previous year questions

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

1
2017 · Mathematics · Calculus · Indefinite Integration
KCET 2017

$$\int \sqrt{x^2+2 x+5} d x \text { is equal to }$$

A

\(\frac{1}{2}(x+1) \begin{aligned} & \sqrt{x^2+2 x+5}+2 \log \mid x+1+ \sqrt{x^2+2 x+5 \mid}+C \end{aligned}\)

B

$\left.(x+1) \sqrt{x^2+2 x+5}+\frac{1}{2} \log \right\rvert\, x+1+\sqrt{x^2+2 x+5}+C $

C

$(x+1) \sqrt{x^2+2 x+5}+2 \log \mid x+1+\sqrt{x^2+2 x+5}+C $

D

$(x+1) \sqrt{x^2+2 x+5}-2 \log \mid x+1+\sqrt{x^2+2 x+5}+C $

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2
2017 · Mathematics · Calculus · Indefinite Integration
KCET 2017
$\int \frac{(x+3) e^x}{(x+4)^2} d x$ is equal to
A
$\frac{e^x}{(x+4)^2}+C$
B
$\frac{e^x}{(x+3)}+C$
C
$\frac{1}{(x+4)^2}+C$
D
$\frac{e^x}{(x+4)}+C$
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3
2017 · Mathematics · Calculus · Indefinite Integration
KCET 2017
$\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x$ is equal to
A
$2(\sin x+x \cos \theta)+C$.
B
$2(\sin x-x \cos \theta)+C$
C
$2(\sin x+2 x \cos \theta)+C$
D
$2(\sin x-2 x \cos \theta)+C$
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4
2018 · Mathematics · Calculus · Indefinite Integration
KCET 2018
$\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to
A
$\sin ^{-1}\left(\frac{3 x+1}{2}\right)+C$
B
$\sin ^{-1}\left(\frac{3 x+1}{6}\right)+c$
C
$\frac{1}{3} \sin ^{-1}\left(\frac{3 x+1}{2}\right)+C$
D
$\sin ^{-1}\left(\frac{2 x+1}{3}\right)+C$
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5
2018 · Mathematics · Calculus · Indefinite Integration
KCET 2018
$\int e^{\sin x} \cdot\left(\frac{\sin x+1}{\sec x}\right) d x$ is equal to
A
$\sin x \cdot e^{\sin x}+C$
B
$\cos x \cdot e^{\sin x}+C$
C
$e^{\sin x}+C$
D
$e^{\sin x}(\sin x+1)+C$
Open complete paper
6
2018 · Mathematics · Calculus · Indefinite Integration
KCET 2018
$\int \frac{1}{1+e^x} d x$ is equal to
A
$\log _e\left(\frac{e^x+1}{e^x}\right)+C$
B
$\log _e\left(\frac{e^x-1}{e^x}\right)+C$
C
$\log _e\left(\frac{e^x}{e^x+1}\right)+C$
D
$\log _e\left(\frac{e^x}{e^x-1}\right)+C$
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7
2019 · Mathematics · Calculus · Indefinite Integration
KCET 2019

$$\int x^3 \sin 3 x d x=$$

A
\(-\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}+\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C\)
B
\(-\frac{x^3 \cdot \cos 3 x}{3}-\frac{x^2 \sin 3 x}{3}+\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C\)
C
\(-\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}-\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C\)
D
\(\frac{x^3 \cdot \cos 3 x}{3}+\frac{x^2 \sin 3 x}{3}-\frac{2 x \cos 3 x}{9} -\frac{2 \sin 3 x}{27}+C\)
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8
2019 · Mathematics · Calculus · Indefinite Integration
KCET 2019

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$

Then \(A, B, C\) are respectively

A
\(\frac{1}{6}, \frac{-1}{3}, \frac{1}{3}\)
B
\(\frac{-1}{6}, \frac{1}{3}, \frac{1}{3}\)
C
\(\frac{-1}{6}, \frac{-1}{3}, \frac{1}{2}\)
D
\(\frac{1}{6}, \frac{1}{3}, \frac{1}{5}\)
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9
2019 · Mathematics · Calculus · Indefinite Integration
KCET 2019

$$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$

A
\(\tan ^{-1} \sqrt{x}+C\)
B
\(2 \log (\sqrt{x}+1)+C\)
C
\(2 \tan ^{-1} \sqrt{x}+C\)
D
\(\frac{1}{2} \tan ^{-1} \sqrt{x}+C\)
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10
2020 · Mathematics · Calculus · Indefinite Integration
KCET 2020

The value of \(\int \frac{1+x^4}{1+x^6} d x\) is

A
\(\tan ^{-1} x+\tan ^{-1} x^3+C\)
B
\(\tan ^{-1} x+\frac{1}{3} \tan ^{-1} x^3+C\)
C
\(\tan ^{-1} x-\frac{1}{3} \tan ^{-1} x^3+C\)
D
\(\tan ^{-1} x+\frac{1}{3} \tan ^{-1} x^2+C\)
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11
2020 · Mathematics · Calculus · Indefinite Integration
KCET 2020

The value of \(\int e^{\sin x} \sin 2 x d x\) is

A
\(2 e^{\sin x}(\sin x-1)+C\)
B
\(2 e^{\sin x}(\sin x+1)+C\)
C
\(2 e^{\sin x}(\cos x+1)+C\)
D
\(2 e^{\sin x}(\cos x-1)+C\)
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12
2020 · Mathematics · Calculus · Indefinite Integration
KCET 2020

If \(\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C\), then the values of \(A, B\) and \(C\) are respectively

A
\(5,-7,-5\)
B
\(2,-7,-5\)
C
\(5,-7,5\)
D
\(2,-7,5\)
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13
2021 · Mathematics · Calculus · Indefinite Integration
KCET 2021

\(\int \frac{x^3 \sin \left(\tan ^{-1}\left(x^4\right)\right)}{1+x^8} d x\) is equal to

A
\(\frac{-\cos \left(\tan ^{-1}\left(x^4\right)\right)}{4}+C\)
B
\(\frac{\cos \left(\tan ^{-1}\left(x^4\right)\right)}{4}+C\)
C
\(\frac{-\cos \left(\tan ^{-1}\left(x^3\right)\right)}{3}+C\)
D
\(\frac{\sin \left(\tan ^{-1}\left(x^4\right)\right)}{4}+C\)
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14
2021 · Mathematics · Calculus · Indefinite Integration
KCET 2021

The value of \(\int e^x\left[\frac{1+\sin x}{1+\cos x}\right] d x\) is equal to

A
\(e^x \tan \frac{x}{2}+C\)
B
\(e^x \tan x+C\)
C
\(e^x(1+\cos x)+C\)
D
\(e^x(1+\sin x)+C\)
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15
2021 · Mathematics · Calculus · Indefinite Integration
KCET 2021

The value of \(\int \frac{x^2 d x}{\sqrt{x^6+a^6}}\) is equal to

A
\(\log \left|x^3+\sqrt{x^6+a^6}\right|+C\)
B
\(\log \left|x^3-\sqrt{x^6+a^6}\right|+C\)
C
\(\frac{1}{3} \log \left|x^3+\sqrt{x^6+a^6}\right|+C\)
D
\(\frac{1}{3} \log \left|x^3-\sqrt{x^6+a^6}\right|+C\)
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16
2021 · Mathematics · Calculus · Indefinite Integration
KCET 2021

The value of \(\int \frac{x e^x d x}{(1+x)^2}\) is equal to

A
\(e^x(1+x)+C\)
B
\(e^x\left(1+x^2\right)+C\)
C
\(e^x(1+x)^2+C\)
D
\(\frac{e^x}{1+x}+C\)
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17
2022 · Mathematics · Calculus · Indefinite Integration
KCET 2022

If \(\int \frac{d x}{(x+2)\left(x^2+1\right)}=a \log \left|1+x^2\right|+b \tan ^{-1} x +\frac{1}{5} \log |x+2|+c,\) then

A
\(a=\frac{-1}{10}, b=\frac{2}{5}\)
B
\(a=\frac{1}{10}, b=\frac{2}{5}\)
C
\(a=\frac{-1}{10}, b=\frac{-2}{5}\)
D
\(a=\frac{1}{10}, b=\frac{-2}{5}\)
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18
2022 · Mathematics · Calculus · Indefinite Integration
KCET 2022

\(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\) is equal to

A
\(2(\sin x-x \cos \alpha)+c\)
B
\(2(\sin x+x \cos \alpha)+c\)
C
\(2(\sin x-2 x \cos \alpha)+c\)
D
\(2(\sin x+2 x \cos \alpha)+c\)
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19
2023 · Mathematics · Calculus · Indefinite Integration
KCET 2023

\(\int \sqrt{\operatorname{cosec} x-\sin x} d x\) is equals to

A
\(\frac{\sqrt{\sin x}}{2}+C\)
B
\(2 \sqrt{\sin x}+C\)
C
\(\frac{2}{\sqrt{\sin x}}+C\)
D
\(\sqrt{\sin x}+C\)
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20
2023 · Mathematics · Calculus · Indefinite Integration
KCET 2023

\(\int \sqrt{5-2 x+x^2} d x\) is equals to

A
\(\begin{aligned} \frac{x}{2} \sqrt{5-2 x+x^2} & +4 \log \mid(x+1)+\sqrt{x^2-2 x+5} \mid+C\end{aligned}\)
B
\(\frac{x-1}{2} \sqrt{5+2 x+x^2}+2 \log \mid(x-1)+\sqrt{5+2 x+x^2} \mid+C\)
C
\(\frac{x-1}{2} \sqrt{5-2 x+x^2}+2 \log \mid(x-1)+\sqrt{5-2 x+x^2} \mid+C\)
D
\(\frac{x-1}{2} \sqrt{5-2 x+x^2}+2 \log \mid(x+1)+\sqrt{x^2+2 x+5}|+C\)
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Showing 20 of 26 questions