Evaluate the integral?

Question

Evaluate the indefinite integral. (Remember to use ln |u| where appropriate.)
t * sec^2(2t) dt

Answer 1

Using by parts

 

u=t  and  v'=

u'=1  and v=(tan2t)/2)

 

                   =t tan2t/2-1/2(-lncos2t/2)+C

                    =t tan2t/2+1/4(lncos2t)+C