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

TL;DR

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

Key Insights

• 🥳 Integration by parts is a method used to find the integral of a product of two functions.
• 🎓 The formula for integration by parts is the integral of u dv equals u times v minus the integral of v du.
• 🛫 When using integration by parts, it is important to choose u and dv strategically.
• 🥳 Integration by parts may require multiple steps involving differentiation and integration.
• 🥳 Like terms can be combined when solving for the integral using integration by parts.
• ☺️ The integral of e to the x is e to the x plus a constant.
• ☺️ The integral of sine x is negative cosine x.

Transcript

in this lesson we're going to find the integral of e to the x sine x dx and so for this problem we're going to use the integration by parts method so the formula is the integral of u dv is equal to u times v minus the integral of v d u so we're going to set u equal to e to the x and then dv we're going to make that equal to sine x dx now d u the de... Read More

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.