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Numerade Educator

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Problem 46 Hard Difficulty

Evaluate the indefinite integral.

$ \displaystyle \int x^2 \sqrt{2 + x} \, dx $

Answer

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

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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.