# Indefinite Integration · Mathematics · AP EAPCET

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AP EAPCET 2021 - 20th August Morning Shift
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
AP EAPCET 2021 - 20th August Morning Shift
$$\int \frac{\sin \alpha}{\sqrt{1+\cos \alpha}} d \alpha$$ is equal to
AP EAPCET 2021 - 20th August Morning Shift
If $$\int \frac{\cos 4 x+1}{\cot x-\tan x}=k \cos 4 x+C$$, then $$k$$ is equal to
AP EAPCET 2021 - 20th August Morning Shift
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
AP EAPCET 2021 - 20th August Morning Shift
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
AP EAPCET 2021 - 19th August Evening Shift
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
AP EAPCET 2021 - 19th August Evening Shift
$$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$$ is equal to
AP EAPCET 2021 - 19th August Evening Shift
$$\int(\cos x) \log \cot \left(\frac{x}{2}\right) d x$$ is equal to
AP EAPCET 2021 - 19th August Evening Shift
$$\int \sqrt{e^{4 x}+e^{2 x}} d x$$ is equal to
AP EAPCET 2021 - 19th August Evening Shift
If $$\int \frac{1}{1+\sin x} d x=\tan (f(x))+c$$, then $$f^{\prime}(0)$$ is equal to
AP EAPCET 2021 - 19th August Morning Shift
$$\int \frac{e^x(x+3)}{(x+5)^3} d x$$ is equal to
AP EAPCET 2021 - 19th August Morning Shift
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
AP EAPCET 2021 - 19th August Morning Shift
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 t...
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