Match exponential derivatives and bases

Integrate with respect to $x$: (a) $2e^{2x-1}$; (b) $3xe^{x^2-1}$; (c) $\sqrt{e^x}-\frac1{\sqrt{e^x}}$; (d) $\frac{e^{\sin^{-1}x}}{\sqrt{1-x^2}}$; (e) $x^3 5^{1-x^4}$.