the second integral by parts

let dv be sec tan and u tan so we will have

how to integrate here multiply the denominator and the nominator by

the nominator is the derivative of denominator so ln(denominator)

since

about the limits if u write ur integral result using t variable there is no need to change the limits since t limits u have it but if u do not write the result using t variable ( theta variable ) then u need to find the limits of theta