Indefinite Integral: How to Use Trig Substitution?

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brandon hodoan
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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


Photo of handwritten calculus work on lined paper: problem 2 asks for the indefinite integral of x^2/(1+x^2) dx using trigonometric substitution, with a right triangle sketch and several crossed-out steps.
 
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##.