Integration by Parts — Step by Step (with Examples)

Learn Integration by Parts step by step with five worked examples. The formula, how to choose u and dv using the LIATE rule, and when to apply the technique twice. Covers the cyclic integral trick where the integral comes back to itself.

Examples include: x*e^x, x*cos(x), ln(x), x^2*e^x (double integration by parts), and e^x*sin(x) (cyclic method). Common mistakes are covered at the end so you know what to avoid on exams.

TIMESTAMPS
0:00 Introduction
0:16 The Formula — ∫u dv = uv - ∫v du
0:49 Choosing u and dv — the LIATE Rule
1:26 Example 1 — ∫x·e^x dx
2:16 Example 2 — ∫x·cos(x) dx
2:53 Example 3 — ∫ln(x) dx
3:39 Example 4 — ∫x²·e^x dx (double IBP)
4:35 Example 5 — ∫e^x·sin(x) dx (cyclic)
5:41 Common Mistakes to Avoid
6:15 Recap

This video is part of a calculus series covering integration techniques. Subscribe to Grasp Maths for more step-by-step math tutorials: https://www.youtube.com/@GraspMaths?sub_confirmation=1

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Видео Integration by Parts — Step by Step (with Examples) канала Grasp Mathematics