# Integral using substitution

1. Dec 5, 2011

### Miike012

∫(1+x)/(1+x^2) dx = ...

I have tryed multiple time using u substitution letting u = 1+ x.... 1 + x^2... x ..x^2 but I can't get any of them to work.

2. Dec 5, 2011

### Dick

Not surprising. Split the integral up into 1/(1+x^2) and x/(1+x^2). You need a different substitution for each part. One is a trig sub. The other isn't. They are different.

3. Dec 6, 2011

### Miike012

is it u = 1+x^2 and u = arctan(x)?

4. Dec 6, 2011

### Miike012

got it thank you.

5. Dec 6, 2011

### 1MileCrash

With a problem like that, either use partial fractions (if numerator power is lesser) or use polynomial long division (and then partial fractions on the remainder, if needed.)

It's always been beneficial to me.