← MATH 01131 · Calculus II
MATH 01131 · Advanced integration
Integration by parts
Definition
∫ u dv = uv − ∫ v du. Choose u to get simpler after differentiating (LIATE: Log, Inverse trig, Algebraic, Trig, Exp).
Read this
Pick u so du is nicer; pick dv so v is easy to integrate.
Sometimes parts twice returns the original integral — solve algebraically for it (e.g. ∫ eˣ sin x).
Tabular method speeds repeated parts for polynomials × exp/sin/cos.
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Try this
Attempt each problem first, then open the worked solution.
1.Compute ∫ x ln x dx and ∫ eˣ cos x dx.