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Question

Integrate:tanxsinxcosxdx.

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Solution

Consider the given integral.

I=tanxsinxcosxdx

I=tanxtanxcosx1secxdx

I=sec2xtanxtanxdx

I=sec2xtanxdx

Let t=tanx

dt=sec2xdx

Therefore,

I=1tdt

I=2t+C

On putting the value of t, we get

I=2tanx+C

Hence, this is the answer.


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