Integration by parts for ln(x²+1) from 0 to 1

[rey242]

Homework Statement

Evaluate the Definite Integral
Integral[0,1] Ln(x^2+1) dx

Homework Equations

The Attempt at a Solution

So far I have done the first part,
U= Ln (x^2+1) Du= 2x/(x^2+1)dx
Dv= 1 dx V=x

x* Ln(x^2+1)- Integral [0,1] (2x^2/(x^2+1) dx

But I'm stuck on the second integral, I have tried punching into a TI-89, but It comes out to a weird answer. Can someone help?

 

[Dick]

Start by dividing the polynomial x^2+1 into x^2 to express it as quotient and remainder.

 

[rey242]

What do I do after that? How does that help?

 

[Dick]

x^2/(1+x^2)=1-1/(1+x^2). You can integrate 1 and you should be able to integrate 1/(1+x^2). It's an inverse trig function.

 

[rey242]

Oh wow, thanks!