Integration by Parts

What would be the value of  $\int \left(x\log 2x\right)dx$

Integrate  ${\displaystyle \int \frac{x^3+\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}3x+2}{{(x^2+1)}^2(x+1)}dx}$

Evaluate the integral $\int \left(x\sin x\right)dx$.

$\int e^{3x}\sin \left(4x+5\right)dx=$

Prove that $\int \sqrt{a^2-x^2}dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}{\sin }^{-1}\left(\frac{x}{a}\right)+c$

Integrate the following function w.r. t. $x$:

$\frac{e^x}{x}\left[x·(\log x{)}^2+2·\log x\right]$

If integration of $x \log x$ with respect to $x$ is $\frac{x^2}{m}\log x-\frac{x^2}{n}+C$, then the value of $m+n$ is

If integration of $25x{e}^{-5x}$ respect to $x$ is $Ax{e}^{-5x}+B{e}^{-5x}+C$, then the value of $A+B$ is 

Evaluate $\int x{e}^{x}dx$.

Find: $\int e^x\sin x dx$

Find $\int e^{ax}·\sin (bx+c)dx$

Find $\int \frac{(x-3)e^x}{(x-1{)}^3}dx$

Find $\int x {\sec }^{2}x dx$.

Evaluate $\int x\log xdx$

Evaluate ${\int }_0^{2\pi }{e}^x·\sin \left(\frac{\pi }{4}+\frac{x}{2}\right)dx$.

Find $\int x·\log xdx$

If $\int e^x\left(\frac{x^2-8x+19}{(x-1{)}^5}\right)dx=\frac{e^x\left(lx+m\right)}{\left(x-1\right){}^4}+C$, then $4l+m=$