Calculus
Advanced

Integration by Parts

Integration technique from the product rule.

Formula

∫u dv=uv−∫v du\int u\,dv = uv - \int v\,du

Variables

u, vDifferentiable functions

Example

∫ x·e^x dx = x·e^x − ∫ e^x dx = e^x(x − 1) + C.

Did You Know?

Integration by parts is the reverse of the product rule — it trades one integral for an easier one.

integralparts