How do you integrate $(sinx+secx)/tanx$ ?

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Answer 1 · 2018-03-15T18:24:41

Rewrite
$int((sinx+1/cosx)/(sinx/cosx))dx$

$=int(((sinxcosx+1)/cancelcosx)/(sinx/cancelcosx))dx$

$=int(((cancelsinxcosx)/cancelsinx)+1/sinx)dx$

$=int(cosxdx)+int(cscxdx)$

Now both of these are standard integrals

$=sinx-ln(csc(x)+cot(x)) +$ Constant

How do you integrate (sinx+secx)/tanx (sinx+secx)/tanx ?