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## Homework Statement

the integral of x^3 (x^2 + 20)^1/2

## Homework Equations

use u substitution

## The Attempt at a Solution

I think I have finally figured the problem out, can you confirm if this is the correct answer please?

u=x^2 +20 x= sqrt(u-20)

du= 2x dx

integral of x^3 * sqrt( u) du/2x

cancel the x's and move the 1/2 in front of the integral

plug in the sqrt(u-20) for x

1/2 integral of (sqrt(u-20))^2 * sqrt(u) du

1/2 integral of u-20 * sqrt(u) du

now I distribute the sqrt(u) to the (u-20) and get

1/2 integral of u^3/2 - 2u^1/2

then I integrated getting

1/2[2/5u^5/2 - 4/3u^3/2]

finally getting 1/2[2/5(x^2+20)^5/2 - 4/3 (x^2+20)^3/2] + C

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