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Question

What is the integral of tan2x?


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Solution

Find the integral of tan2x.

Let 2x=u.

So, 2dx=du

Put the above value intan2xdx:

tan2xdx=12tanudutan2xdx=12ln|secu|+Ctanudu=ln|secu|+Ctan2xdx=12ln|sec2x|+C{u=2x}

Hence, the required integral is tan2xdx=12ln|sec2x|+C where C is a constant.


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