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Numerade Educator

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Problem 3 Easy Difficulty

Evaluate the integral by making the given substitution.

$ \displaystyle \int x^2 \sqrt{x^3 + 1} \, dx $, $ u = x^3 + 1 $

Answer

$$\frac{2}{9}\left(x^{3}+1\right)^{3 / 2}+C$$

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Video Transcript

Okay, We've been told that you is x cubed plus one, which means I'm gonna take the derivative we get D'You is three x squared DX which means d axe is do you divide it by three X square? Okay, Now that we have this, we know that we can integrate and we know we have integral X squared times Spurt of x cubed plus three. So use the power rule which is increase the exploding by Juan divide by the new experiment. When you're integrating, it's the power rule is in a textbook. This gives us 2/9 times square root of X cubed plus three huge plus c