6) Let u and v be functions of a. (a) Starting with the expression duu) = u de + v du show that:dz \int u \frac{d v}{d x} d x=u

v-\int v \frac{d u}{d x} d x (b) Find the indefinite integrals: \text { (i) } \int x e^{4 a x} d x \text { (ii) } \int x \sin (x) d x \text { (iii) } \int x^{2} e^{-4 x} d x