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Numerade Educator

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Problem 48 Hard Difficulty

Evaluate the indefinite integral.

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

Answer

$\frac{1}{s} \sqrt{\left(n^{2}+1\right)^{5}}-\frac{1}{3} \sqrt{\left(x^{2}+1\right)^{3}}+c$

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Video Transcript

This is the integral we are trying to integrate, which means that we know that you can beat the inside of the square root betweens writing this detox, the derivative is do you over to X and the derivative of one is simply Xerox. It's constant. Therefore, now we can write this oz 1/2 because it's the constant. So it goes on the outside. Integrate us. Remember the exponents increased by one divide by the exponents. This is the power rule outlined in the textbook back. Substitute us X squared plus one. And don't forget your pussy.