Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.1 Integration by Parts, #55 · Calculus · Techniques of integration

Test this rule on

These problems need more than one integration.

Two integrations by parts lead to $V =$ integral of $v$ :

$\int u v^{'} d x = uv - V u^{'} + \int V u^{''} d x$ .

Test this rule on $\int x^{2} sin x d x$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.1 Integration by Parts, #55

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