Integration
Lesson 5 of 11
Integration by parts
Objective. Integrate products using ∫u dv = uv − ∫v du.
The key idea
Choose u to be the part that gets simpler when differentiated — usually a polynomial or a logarithm.
Worked example
Find ∫ x e^x dx.
- 1Let u = x and dv = e^x dx.
- 2Then du = dx and v = e^x.
- 3x e^x − ∫ e^x dx.
Answer: x e^x − e^x + c
Practice
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