List of top Mathematics Questions on Integrals of Some Particular Functions asked in KEAM

$\int (\cot 2x + \csc 2x) dx = $

\(\int \frac{10e^x}{(2e^x + 5)^3} dx\) is equal to 
 

$\int(\sin^{-1}\sqrt{x}+\cos^{-1}\sqrt{x})dx=$ ________.
$\int\frac{\sin 2x}{\sin x}dx=$ ________.
$\int\frac{1+log\,x}{\left(1+x\,log\,x\right)^{2}}dx$ is equal to
If $f\left(x\right) = \int\limits^{sin\,x}_{2x}cos\left(t^{3}\right)dt$, then $f'{x}$ is equal to
$\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} \,dx$ is equal to
$\int\frac{2x+\sin2x}{1+\cos2x}\, dx$ is equal to
$\int\frac{dx}{x-\sqrt{x}}$ is equal to
$\int \limits^{2017}_{2016} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{4033 - x}} dx $ is equal to
$\int\limits_{0}^{1} x e^{-5x} \, dx$ is equal to
$\int\frac{1}{\sin x\, \cos x}$ dx is equal to
$\int\left(\frac{x-a}{x}-\frac{x}{x+a}\right) dx$ is equal to
$ \int{\frac{dx}{\sqrt{1-{{e}^{2x}}}}} $ is equal to
If $\int \frac{f\left(x\right)}{log\,cos\,x}dx=-log\left(log\,cos\,x\right)+C$, then $f\left(x\right)$ is equal to
$ \int{({{\sin }^{6}}x+{{\cos }^{6}}x+3{{\sin }^{2}}x \,{{\cos }^{2}}x)}dx $ is equal to
$ \int_{-1}^{1}{\frac{17{{x}^{5}}-{{x}^{4}}+29{{x}^{3}}-31x+1}{{{x}^{2}}+1}}dx $ is
$\int \frac{e^{x}}{x}\left(x\,log\,x+1\right)dx$ is equal to
$\displaystyle \int^{\sqrt{\pi}/2}_0$ $2x^{3} sin\left(x^{2}\right) dx =$dx is equal to
$\int\frac{3 ^{x}}{\sqrt{1-9 ^{x}}}dx\quad$is equal to
$ \int{(x+1){{(x+2)}^{7}}}(x+3)dx $ is equal to
$ \int{\frac{\sec x cosec x}{2\cot x-\sec x\cos ecx}}dx $ is equal to
$ \int{\frac{{{4}^{x+1}}-{{7}^{x-1}}}{{{28}^{x}}}}dx $ is equal to
$ \int{\frac{\cos x-\sin x}{1+2\sin x\cos x}}dx $ is equal to
$\int \frac{sec\,x\,dx}{\sqrt{cos\,2\,x}}$ is equal to