How to solve some simple integrals (HW)

Question

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

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

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

score 1 · Answer 1 · answered Apr 10 '13 at 21:53

1

Hints:

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

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

answered Apr 10 '13 at 21:53

Git Gud

This porridge is too hot (+1) – robjohn Apr 10 '13 at 21:57
@robjohn Agreed, but I couldn't just edit my answer and copy yours, that's why I kept it like this.But I wouldn't change the first hint. – Git Gud Apr 10 '13 at 21:59
@robjohn I got it. – Git Gud Apr 10 '13 at 22:00
Good – robjohn Apr 13 '13 at 09:08

score 1 · Answer 2 · answered Apr 10 '13 at 21:53

1

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

For the second integral, use partial fraction decomposition.

answered Apr 10 '13 at 21:53

Zev Chonoles

score 1 · Accepted Answer · answered Apr 10 '13 at 21:54

1

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

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

answered Apr 10 '13 at 21:54

robjohn

3 Answers3