💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# Evaluate the indefinite integral. $\displaystyle \int x^2 \sqrt{2 + x} \, dx$

## $\int x^{2} \sqrt{2+x} d x=\frac{2}{7}(2+x)^{7 / 2}-\frac{8}{5}(2+x)^{5 / 2}+\frac{8}{3}(2+x)^{3 / 2}+C$

Integrals

Integration

### Discussion

You must be signed in to discuss.
##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp

### Video Transcript

This is the problem. We've been given the integral X squared times a skirt of two plus acts D x now we have you is two plus acts. Therefore, axe is you minus two. Detox is do you? Which means now we have the integral of humanist two squared time squirt of you, Do you which we know can be written as using the power rule. The expert increases by one We divide by the new exponents. Substitute back in that you is two plus acts symbol for any fractions. And don't forget your posse.

#### Topics

Integrals

Integration

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp