What Substitution Should Be Used to Solve ∫(1+x)/(1+x^2) dx?

[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.

 

[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.

 

[Miike012]

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

 

[Miike012]

got it thank you.

 

[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.