Let u=f(x) and v=g(x) be functions with continuous derivatives. Then, the integration-by-parts formula for the integral involving these two functions is:
∫udv=uv−∫vdu
In the following problem, we will use integration-by-parts to evaluate the indefinite integral
∫xexdx
Part 1.
How should we choose uu and dvdv?
u=
in which case du=
dv=
in which case v=
Note: omit the arbitrary constant in your answer for vv. To see why this is acceptable, check out example 3.1 from the text.