Integral of e^x sinx | Summary and Q&A

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March 15, 2018
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The Organic Chemistry Tutor
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Integral of e^x sinx

TL;DR

This lesson teaches how to find the integral of e to the x sine x using the integration by parts method.

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Questions & Answers

Q: What is the formula for integration by parts?

The formula for integration by parts is the integral of u dv equals u times v minus the integral of v du.

Q: How do you set u and dv in integration by parts?

In integration by parts, you set u as one function and dv as another function. u is usually chosen as a function that becomes simpler when differentiated, while dv is chosen as a function that becomes simpler when integrated.

Q: How do you find the integral of e to the x?

The integral of e to the x is simply e to the x plus a constant. It is obtained by applying the power rule of integration.

Q: What do you do when encountering like terms in the integration by parts process?

When encountering like terms, you can combine them by adding or subtracting them. Like terms have the same variables and exponents.

Summary & Key Takeaways

  • The lesson teaches how to find the integral of e to the x sine x using the integration by parts method.

  • Integration by parts involves the formula: integral of u dv equals u times v minus the integral of v du.

  • The process involves setting u as e to the x and dv as sine x dx, finding the derivatives and integrals, and applying the formula multiple times.

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