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1 8 1 Integration by Parts Recall the Product Rule for Derivatives use u v du and dv d uv Integrate both sides and solve for u dv Therefore u dv This formula is the key to Integration by Parts The key is to choose what part of the integral is to be u and what part is to be dv Examples x cos x dx 1 1 x2 e 2x dx 0 x2 ln x dx 2 On Beyond Average e2x cos 3x dx x5 sin x3 1 dx 2 0 0 3 2 x3 f 0 x dx x2 f x dx 5 What is Suppose f 0 3 f 2 4 and
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