# Integration Problem

## Homework Statement

$$\int {\frac{sin^{2}x}{1+sin^{2}x}dx}$$

## Homework Equations

Let t = tan x/2, then dx = 2/(1+t^2) and sin x = 2t / (1+t^2)

## The Attempt at a Solution

I got up to the point where $$\int {\frac{8t^{2}}{(1+6t^{2}+t^{4})(1+t^{2})} dt}$$. Not sure if I'm on the right track and if I am, do I use partial fractions after this?

The final answer is attached. Can't really make out the handwriting :/

#### Attachments

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$$\int {\frac{2}{1+t^{2}} + {\frac{-2t^{2}-2}{(1+6t^{2}+t^{4})} dt}$$