How do you integrate #int x csc^2x# by integration by parts method?

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Answer 1 · 2018-04-01T08:13:26

The answer is #=-xcotx+ln(|sinx|)+C#

#" Reminder "#

#intcotxdx=ln(|sinx|)+C#

#intuv'=uv-intu'v#

#u=x#, #=>#, #u'=1#

#v'=csc^2x#, #=>#, #v=-cotx#

Therefore,

#intxsec^2xdx=-xcotx+intcotxdx#

#=-xcotx+ln(|sinx|)+C#