Mr. Integral
Math notes/Calculus II/Integration Methods

Integration by Parts — Cheat sheet

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Core rule

∫u dv=uv−∫v du,\int u\,dv=uv-\int v\,du, ∫abu dv=[uv]ab−∫abv du.\int_a^bu\,dv=[uv]_a^b-\int_a^bv\,du.

Watch for

Choose an easier remaining integral, retain the minus sign and boundary term, and solve algebraically when the original integral returns.