< 1 >
Partial integration
The formula for integration by parts is
This formula only makes sense if the integral ∫v du is easier to solve than the original integral ∫u dv.
Explanation
If the functions u (x) and v (x), can be differentiated in the interval (a, b), then the function u (x) · v (x) can also be differentiated in (a, b). The product rule is
Integration of both members gives