.

3.2 Integration by substitution

1.

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

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

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