Question(b) Use your work in (a) to help you evaluate the following indefinite integrals. Use differentiation to check your work. (Don't forget the " $+C^{\text {" }}$.) (i) $\int x e^{x}+e^{x} d x=\left(\mathrm{xe}^{\wedge} \mathrm{x}\right)+\mathrm{C}$ (ii) $\int e^{x}(\sin (x)+\cos (x)) d x=\left(\mathrm{e}^{\wedge} \mathrm{x}\right) \sin (\mathrm{x})+\mathrm{C}$ (iii) $\int 2 x \cos (x)-x^{2} \sin (x) d x=\left(x^{\wedge} 2\right) \sin (x)+2 x \cos (x)-2 \sin (x$. (iv) $\int x \cos (x)+\sin (x) d x=x \sin (x)+C$ (v) $\int 1+\ln (x) d x=x \ln (\mathrm{x})+\mathrm{C}$ $\qquad$ (c) Observe that the examples in (b) work nicely because of the derivatives you were asked to calculate in (a). Each integrand in (b) is precisely the result of differentiating one of the products of basic functions found in (a). To see what happens when an integrand is still a product but not necessarily the result of differentiating an elementary product, we consider how to evaluate