Integration

Integration by Parts
relies on the formula:

$$ \int_a^b f(x)g'(x) dx = [f(x)g(x)]_a^b - \int_a^b f'(x) g(x) dx$$

and that:

$$ [f(x)g(x)]_a^b = f(b) g(b) - f(a) g(a) $$

Integration by Substitution
also like sucking on a dog turd.

The method of integration by substitution is the reverse of the chain rule