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  3. ZuAI AP College Board Calculus AB/BC
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Integrating Using Integration by Parts

Benjamin Wright

Benjamin Wright

7 min read

Next Topic - Integrating Using Linear Partial Fractions
Study Guide Overview

This study guide covers Integration by Parts for AP Calculus BC. It explains the basics of the technique, derived from the product rule, and its formula. It details the strategy for selecting u and dv using the LIATE mnemonic, differentiating, integrating, and solving. Several practice problems demonstrate the application of integration by parts, including examples requiring multiple applications and algebraic manipulation.

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Previous Topic - Integrating Functions Using Long Division and Completing the SquareNext Topic - Integrating Using Linear Partial Fractions

Question 1 of 10

What is the correct formula for Integration by Parts? 🤔

∫u,dv=uv+∫v,du\int u , dv = uv + \int v , du∫u,dv=uv+∫v,du

∫u,dv=uv−∫v,du\int u , dv = uv - \int v , du∫u,dv=uv−∫v,du

∫u,dv=∫v,du−uv\int u , dv = \int v , du - uv∫u,dv=∫v,du−uv

∫uv=∫u,dv−∫v,du\int uv = \int u , dv - \int v , du∫uv=∫u,dv−∫v,du