Originally Posted by

**arbolis** I am stuck on 4 problems involving a substitution to be solved.

It only says it must be solved using a substitution and no other method of solving integrals.

1)$\displaystyle \int \frac{e^x dx}{e^{2x}+2e^x+1}$. I've trying a u-sub : $\displaystyle u(x)=e^x$, also $\displaystyle u(x)=e^{\frac{x}{2}}$ and $\displaystyle u(x)=e^{2x}+2e^x+1$ but in each case I failed to solve it.

2)$\displaystyle \int ln(\cos(x))tan(x)dx$. I don't really know what sub to make here. Maybe $\displaystyle u=\cos (x)$?

3)$\displaystyle \int \frac{dx}{e^x+e^{-x}}$. Making the sub $\displaystyle u(x)=e^x$, I got $\displaystyle \int \frac{dx}{e^x+e^{-x}}=\int \frac{du}{u^2-u}$ but I don't know how to finish it!

4)$\displaystyle \int \frac{dx}{1+e^x}$. I took $\displaystyle u(x)=1+e^x$ and I got an answer very similar to the 3) : $\displaystyle \int \frac{du}{u^2+u}$ but don't know how to finish it.