In the differential equations slides, the equation

$$f(x)+x{f}^{\mathrm{\prime }}(x)=h(x)$$

is solved using the product rule. Which expression below correctly represents the solution shown in the slides?

a) $f(x)=\int h(x)\,dx$
b) $f(x)=\dfrac{\int h(x)\,dx}{x}$
c) $f(x)=x\int h(x)\,dx$
d) $f(x)=h'(x)+x$
e) $f(x)=ce^x$