u-Substitution
The chain rule, read right to left.
Concept
Rename the inside
If the integrand contains a function and (a multiple of) its derivative, let u be that inner function. Then du replaces the leftover factor and the integral simplifies.
For definite integrals, either convert the limits to u-values or convert back to x before evaluating — do not mix the two.
∫ f(g(x))g′(x) dx = ∫ f(u) du