Use the specified substitutions

Use the given substitutions to find the following integrals:

(a) $\displaystyle\int\dfrac1{e^x+e^{-x}}\,dx$, let $u=e^x$.

(b) $\displaystyle\int\dfrac{x+1}{(2x-1)^2}\,dx$, let $u=2x-1$.

(c) $\displaystyle\int\dfrac1{2+\sqrt x}\,dx$, let $u=\sqrt x$.

(d) $\displaystyle\int\sin^3x\,dx$, let $u=\cos x$.

(e) $\displaystyle\int\dfrac{x}{\sqrt{1-x^2}}\,dx$, let $x=\sin\theta$.

(f) $\displaystyle\int\dfrac1{(x^2+1)^2}\,dx$, let $x=\tan\theta$.