Indefinite Integration - PYQs | AP EAPCET Math

\(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x\) is equal to

\(\int(\cos x) \log \cot \left(\frac{x}{2}\right) d x\) is equal to

\(\int \sqrt{e^{4 x}+e^{2 x}} d x\) is equal to

Which of the following is partial fraction of \(\frac{-x^2+6 x+13}{(3 x+5)\left(x^2+4 x+4\right)}\) is equal to

If \(\int \frac{1}{1+\sin x} d x=\tan (f(x))+c\), then \(f^{\prime}(0)\) is equal to

\(\int \frac{e^x(x+3)}{(x+5)^3} d x\) is equal to

If \(\int \frac{(x-1)^2}{\left(x^2+1\right)^2} d x=\tan ^{-1}(x)+g(x)+k\), then \(g(x)\) is equal to

If \(\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\right|+c\), then \(A\) is equal to

If \(f(x)=\frac{1}{\left(\cos ^2 x\right) \sqrt{1+\tan x}}\), then its antiderivative \(F(x)=\) ........, given, \(F(0)=4\)

If the primitive of \(\cos (\log x)\) is \(f(x)\{\cos (g(x))+\sin (h(x))\}\), then which among the following is true?

If

\(\begin{aligned} \[\frac{2 x^4-x^3+3 x^2-x+4}{x^2-3 x+2} =f(x)+\frac{A}{x-1}+\frac{B}{x-2}\end{aligned}\), then\]

If \(f^{\prime}(x)=x+\frac{1}{x}\), then \(f(x)\) is equal to

\(\int \frac{\sec x}{\sqrt{\sin (2 x+\theta)+\sin \theta}} d x\) is equal to

If \(\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C\), then \(k\) is equal to

\(\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha\) is equal to

If \(\int\left[\cos (x) \cdot \frac{d}{d x}(\operatorname{cosec}(x)] d x=f(x)+g(x)+c\right.\) then \(f(x) \cdot g(x)\) is equal to

Given, \(\frac{3 x-2}{(x+1)^2(x+3)}=\frac{A}{x+1} +\frac{B}{(x+1)^2}+\frac{C}{x+3}\), then \(4 A+2 B+4 C\) is equal to

If \(\int \frac{(2 x+1)^6}{(3 x+2)^8} d x=P\left(\frac{2 x+1}{3 x+2}\right)^Q+R\), then \(\frac{P}{Q}\) is equal to

If \(\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K\) then \(A+B+C=\)

If \(f(x)=\int x^2 \cos ^2 x\left(2 x \tan ^2 x-2 x-6 \tan x\right) d x\) and \(f(0)=\pi\), then \(f(x)=\)