How to integrate? #int sec^3 x cot^2 x dx#

1 Answer
mason m
Sep 4, 2017

#-cscx+lnabs(secx+tanx)+C#

Explanation:

#intsec^3xcot^2xdx=int1/cos^3xcos^2x/sin^2xdx=int1/cosx1/sin^2xdx#

#=intsecxcsc^2xdx=intsecx(cot^2x+1)dx#

#=int(1/cosxcos^2x/sin^2x+secx)dx#

#=int(1/sinxcosx/sinx+secx)dx=int(cscxcotx+secx)dx#

#=-cscx+lnabs(secx+tanx)+C#

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