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 $\int \left(x\sin x\right)dx$.

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

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

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 $4l+m=$

Integrate with respect to $\mathrm{x}$:

${\sin }^{-1}\left(\frac{2\mathrm{x}}{1+{\mathrm{x}}^2}\right)$

Integrate with respect to $\mathrm{x}$:

$\frac{\mathrm{x}}{1+\mathrm{sinx}}$

Integrate with respect to $x$:

${\left({\sin }^{-1}x\right)}^2$

Integrate with respect to $x$:

${\cos }^{-1}\left(\frac{1}{x}\right)$

Integrate with respect to $x$:

$\frac{x^2}{(x\cos x-\sin x{)}^2}$