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Question

Evaluate: cos2x+2sin2xcos2xdx.

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Solution

We use the identity cos2x=cos2xsin2x

With the substitution of this expression into the given integral, we get:
cos2x+2sin2xcos2xdx=cos2x+sin2xcos2xdx=1cos2xdx=sec2xdx=tanx+C

where C is a real constant of integration.

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