Integration by parts

Objective. Integrate products using ∫u dv = uv − ∫v du.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: 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.

1 $Let u = x and dv = e^x dx.$
2 $Then du = dx and v = e^x.$
3 $x e^x - \int e^x dx.$

Answer: x e^x − e^x + c

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