For the first integral, let u=tan(5x)\(\displaystyle \L\int\)sec4(5x)dx
My work so far:
\(\displaystyle \L\;\;\int\)[tan2(5x)+1][sec2(5x)]dx
\(\displaystyle \L\;\;\int\)\(\displaystyle \tan^2(5x)\cdot\sec^2(5x)\,dx\;+\;\L\int\)sec2(5x)dx . . . good!