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How to Solve Integrals Using Integration By Parts (Calculus 2 Lesson 11)

In this video we learn about a new technique for solving integrals that we previously could not integrate. This technique is known as integration by parts, and is useful for integrating products of functions of various types, including logarithmic functions, exponential functions, algebraic functions, trig functions, and inverse trig functions. We discuss the origin of the formula for integration by parts, and how to use it for different integrals. This includes determining how to choose u and dv from an integral based on certain criteria, and then using those values to simplify and solve that integral.

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This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 Why Integration By Parts?
2:15 Deriving the Formula
6:20 Integration By Parts Formula
7:03 Example - x*e^x
12:02 Example - x*sinx
15:40 Trick For Choosing u
17:39 Example - x*lnx
21:22 Example - lnx
23:37 Example - x^2*cosx
30:03 Example - e^x*sinx
38:06 Example - x*cosx from 0 to pi
41:12 Outro


📝 Examples Video:    • Integration By Parts Examples | Calculus 2...  

⏩ Next Lesson:    • Tabular Method - Integration By Parts | Ca...  

📺 Calculus 2 Playlist:    • Calculus 2  

📺 Calculus 1 Playlist:    • Calculus 1  


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