How do you integrate $sechx (tanhx-sechx) dx$ ?

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Answer 1 · 2016-04-21T11:13:58

$sechx-tanhx+C$

If we distribute the $sechx$ term, we get

$=int(sechxtanhx-sech^2x)dx$

Splitting this into two integrals:

$=intsechxtanhxdx-intsech^2xdx$

Recall that $(sechx)'=sechxtanhx$ and $(tanhx)'=sech^2x$ .

Thus, the integral gives us:

$=sechx-tanhx+C$

How do you integrate sechx (tanhx-sechx) dxsechx (tanhx-sechx) dx?