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Question

Integrate the function 11tanx

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Solution

Let I=11tanxdx
=cosxcosxsinxdx
=122cosxcosxsinxdx
=12(cosxsinx)+(cosx+sinx)(cosxsinx)dx
=121dx+12cosx+sinxcosxsinxdx
=x2+12cosx+sinxcosxsinxdx
Put cosxsinx=t(sinxcosx)dx=dt
I=x2+12(dt)t
=x212log|t|+C
=x212log|cosxsinx|+C

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