.

3.3 Integration by parts

1.

(a) $${xe^{x} - e^{x} + C}$$ (b) $${-x\cos{x} + \sin{x} + C}$$ (c) $${\frac{1}{4}e^{2x}(2x - 1) + C}$$

(d) $${(x^{2} - 2x + 2)e^{x} + C}$$

(e) $${(2-x^{2})\cos{x} + 2x\sin{x} + C}$$ (f) $${\frac{1}{3}e^{x^{3}}(x^{3} - 1) + C}$$

(g) $${x\sin{x} + \cos{x} + C}$$