Trigonometric identities and reverse chain rules

Find the following integrals:

(a) $\displaystyle\int \sec^2(5x)\tan^3(5x)\,dx$

(b) $\displaystyle\int \dfrac{\sin y}{1+2\cos y}\,dy$

(c) $\displaystyle\int e^x\operatorname{cosec}^2(e^x)\,dx$

(d) $\displaystyle\int \tan^2(2t)\,dt$

(e) $\displaystyle\int \dfrac1{1-\cos2x}\,dx$.