Question

Integrate:

Answer 1

\[\LARGE \int_{0}^{\pi}~cos^4(2t)~dt\]

Answer 2

see enclosed

Answer 3

you can write cos^4 (2t)=(1- sin^2 (2t)) cos^2 (2t)=cos^2 (2t)- cos^2 (2t) sin^2 (2t)=[cos 4t+1]/2 - sin^2 (4t)/4.. similarly write sin^2 4t as cos 8t term.. do the rest