Integration by parts, checked

You will check formulas that come from integration by parts, by taking slopes on the computer. A formula is an antiderivative when its slope equals the integrand everywhere you test.

The idea. By parts, $\displaystyle\int x\,e^{kx}\,dx = e^{kx}\left(\dfrac{x}{k} - \dfrac{1}{k^2}\right)$. Using parts twice gives $\displaystyle\int x^2e^{kx}\,dx = e^{kx}\left(\dfrac{x^2}{k} - \dfrac{2x}{k^2} + \dfrac{2}{k^3}\right)$.

Your tasks.

1. Finish slope(F, x). Return the estimate $\dfrac{F(x + h) - F(x - h)}{2h}$ with h = H.
2. Finish first_formula(k). Return a function of x that is the formula for $\int x\,e^{kx}\,dx$ above.
3. Finish second_formula(k). Return a function of x that is the formula for $\int x^2e^{kx}\,dx$ above.