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Numerade Educator

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Problem 7 Easy Difficulty

Evaluate the indefinite integral.

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

Answer

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

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Video Transcript

Okay, We've been given this problem that you is one highest explored. Take the derivative. In other words, do you? We got negative two ex DX, which means writing this in terms of x t X. We have negative 1/2 to you. Okay, Now I'm taking the integral. We know we can pull the constant negative half out. Use the power all for integration, which is increased the explain it by one divide by the new X Poona Now back substitute. And because we don't want you in our final solution and we have our integral