# U substitution problem?

so the problem is x³√(x²+24)

what would I make u because either one I wouldn't know how to make it work.

Update:

sorry I meant x³√(x² 24)dx obviously

### 1 Answer

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- 6 years agoBest Answer
u = x^2 + 24

du = 2x * dx

x^3 * sqrt(x^2 + 24) * dx =>

x^2 * sqrt(x^2 + 24) * x * dx =>

(u - 24) * sqrt(u) * (1/2) * du =>

(1/2) * u^(3/2) * du - 12 * u^(1/2) * du

Integrate

(1/2) * (2/5) * u^(5/2) - 12 * (2/3) * u^(3/2) + C =>

(1/5) * u^(5/2) - 8 * u^(3/2) + C =>

(1/5) * u^(3/2) * (u^(2/2) - 40) + C =>

(1/5) * (u - 40) * u^(3/2) + C =>

(1/5) * (x^2 + 24 - 40) * (x^2 + 24)^(3/2) + C =>

(1/5) * (x^2 - 16) * (x^2 + 24)^(3/2) + C

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