$\int \frac{2 x-1}{2 x+3} d x=x-\log \left|(2 x+3)^2\right|+C$

$\int \frac{2 x+3}{x^2+3 x} d x=\log \left|x^2+3 x\right|+C$

$\int \frac{\left(x^2+2\right) d}{x+1} x$

$\int \frac{e^{6 \log x}-e^{5 \log x}}{e^{4 \log x}-e^{3 \log x}} d x$

$\int \frac{(1+\cos x)}{x+\sin x} d x$

$\int \frac{d x}{1+\cos x}$

$$\int \tan ^2 x \sec ^4 x d x$$

$\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x$

$\int \sqrt{1+\sin x} d x$

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

$\int \sqrt{\frac{a+x}{a-x}} d x$

$\int \frac{x^{1 / 2}}{1+x^{3 / 4}} d x$

$\int \frac{\sqrt{1+x^2}}{x^4} d x$

$\int \frac{d x}{\sqrt{16-9 x^2}}$

$\int \frac{d t}{\sqrt{3 t-2 t^2}}$

$\int \frac{3 x-1}{\sqrt{x^2+9}} d x$

$\int \sqrt{5-2 x+x^2} d x$

$\int \frac{x}{x^4-1} d x$

$\int \frac{x^2}{1-x^4} d x$

$\int \sqrt{2 a x-x^2} d x$

$\int \frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 4}} d x$

$\int \frac{(\cos 5 x+\cos 4 x)}{1-2 \cos 3 x} d x$

$\int \frac{\sin ^6 x+\cos ^6 x}{\sin ^2 x \cos ^2 x} d x$

$\int \frac{\sqrt{x}}{\sqrt{a^3-x^3}} d x$

$\int \frac{\cos x-\cos 2 x}{1-\cos x} d x$

$\int \frac{d x}{x \sqrt{x^4-1}}$

$\int_0^2\left(x^2+3\right) d x$

$\int_0^2 e^x d x$

$\int_0^1 \frac{d x}{e^x+e^{-x}}$

$\int_0^{\pi / 2} \frac{\tan x}{1+m^2 \tan ^2 x} d x$

$\int_1^2 \frac{d x}{\sqrt{(x-1)(2-x)}}$

$$\int_0^1 \frac{x}{\sqrt{1+x^2}} d x$$

$\int_0^\pi x \sin x \cos ^2 x d x$

$\int_0^{1 / 2} \frac{d x}{\left(1+x^2\right) \sqrt{1-x^2}}$

$\int \frac{x^2}{x^4-x^2-12} d x$

$\int \frac{x^2}{\left(x^2+a^2\right)\left(x^2+b^2\right)} d x$

$\int_0^\pi \frac{x}{1+\sin x}$

$\int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x$

$\int e^{\tan ^{-1} x}\left(\frac{1+x+x^2}{1+x^2}\right) d x$

$\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x$

$\int_{\pi / 3}^{\pi / 2} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{5 / 2}} d x$

$\int e^{-3 x} \cos ^3 x d x$

$\int \sqrt{\tan x} d x$

$\int_0^{\pi / 2} \frac{d x}{\left(a^2 \cos ^2 x+b^2 \sin ^2 x\right)^2}$

$\int_0^1 x \log (1+2 x) d x$

$\int_0^\pi x \log \sin x d x$

$\int_{\pi / 4}^{\pi / 4} \log (\sin x+\cos x) d x$

$\int \frac{\cos 2 x-\cos 2 \theta}{\cos x-\cos \theta} d x$ is equal to

$\frac{d x}{\sin (x-a) \sin (x-b)}$ is equal to

$\int \tan ^{-1} \sqrt{x} d x$ is equal to

$\int \frac{x^9}{\left(4 x^2+1\right)^6} d x$ is equal to

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

$\int \frac{x^3}{x+1}$ is equal to

$\int \frac{x+\sin x}{1+\cos x} d x$ is equal to

If $\frac{x^3 d x}{\sqrt{1+x^2}}=a\left(1+x^2\right)^{3 / 2}+b \sqrt{1+x^2}+C$, then

$\int_{-\pi / 4}^{\pi / 4} \frac{d x}{1+\cos 2 x}$ is equal to

$\int_0^{\pi / 2} \sqrt{1-\sin 2 x} d x$ is equal to

$\int_0^{\pi / 4} \cos x e^{\sin x} d x$ is equal to

$\int \frac{x+3}{(x+4)^2} e^x d x$ is equal to

If $\int_0^a \frac{1}{1+4 x^2} d x=\frac{\pi}{8}$, then $a=$ ............. .

$\int \frac{\sin x}{3+4 \cos ^2 x} d x=$ ........... .

The value of $\int_{-\pi}^\pi \sin ^3 x \cos ^2 x d x$ is ............. .