How to solve some simple integrals (HW)

Question

I'm stuck with those integrals. Can you give me a hint how to start solving?

$$\int{\frac{\ln(x+1)}{x+1}}dx$$

$$\int{\frac{1}{x^2-1}}dx$$

Answer 1

Hint: try the substitution $u=\log(x+1)$

Hint: use partial fractions to write $\dfrac1{x^2-1}=\dfrac A{x-1}+\dfrac B{x+1}$

Answer 2

Hints:

$\bullet (\displaystyle \ln (x+1))'=\frac{1}{x+1}$

$\bullet \displaystyle \frac{1}{x^2-1}=\frac{1/2}{x-1}-\frac{1/2}{x+1}$

Answer 3

For the first integral, use $u$-substitution.

For the second integral, use partial fraction decomposition.