3.2 Integration by substitution

1.

(a) $\displaystyle{-\frac{1}{2}\cos{(2x)} + C}$ (b) $\displaystyle{\frac{1}{2}\log(x^{2} + 1) + C}$ (c) $\displaystyle{\frac{1}{2}e^{2x} + C}$ (d) $\displaystyle{\log\vert\log{x}\vert + C}$

(e) $\displaystyle{\frac{1}{2}e^{x^{2}} + C}$ (f) $\displaystyle{\frac{1}{3}\sin^{3}{x} + C}$ (g) $\displaystyle{2\left(\frac{(1+x)^{5/2}}{5} - \frac{(1+x)^{3/2}}{3}\right) + C}$

(h) $\displaystyle{\log\vert\sin{x} + \cos{x}\vert + C}$ (i) $\displaystyle{\log(1 + e^{x}) + C}$