$$\int \frac{x-3}{(x-1)^3} e^x d x=$$

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

If $$I=\int \frac{e^x}{e^{4 x}+e^{2 x}+1} d x$$ and $$J=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x$$, then for any arbitrary constant $$C$$, than the value of $$J-I$$ equals

If $$\mathrm{I}=\int \frac{2 x-7}{\sqrt{3 x-2}} \mathrm{~d} x$$, then $$\mathrm{I}$$ is given by