Indefinite Integral: How to Use Trig Substitution?

[brandon hodoan]

Homework Statement

Find the indefnite integral using trig substitution.
∫[(x^2) / (1+x^2)]dx

Homework Equations

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The Attempt at a Solution

 

[Delta2]

The denominator should be $sec^2(\theta)$ so all you left with is $\int tan^2\theta d\theta$. To calculate that make the substitution $x=tan\theta$ and notice that $dx=(1+tan^2\theta)d\theta$.