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Question

What is the integral for tanx?


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Solution

Find the integral for tanx.

Use tanx=sinxcosx.

tanxdx=sinxcosxdx

Let cosx=u. So, -sinxdx=du

tanxdx=-duutanxdx=-lnu+CCisaconstant.tanxdx=-lncosx+Ctanxdx=lncosx-1+Ctanxdx=lnsecx+C

Hence, the integral of tanxis lnsecx+C where C is a constant.


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