What is the integral of (x^2)/(sqrt(5-x^3)) ?

The integral of (x^2)/(sqrt(5-x^3)) is -2/3 sqrt(5-x^3)+C

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integral of (x^2)/(sqrt(5-x^3))

\int \frac{x ^{2}}{5 - x ^{3}} d x

- \frac{2}{3} 5 - x^{3} + C

Solution steps

\int \frac{x ^{2}}{5 - x ^{3}} d x

Apply u-substitution

: \int - \frac{2}{3} d u

= \int - \frac{2}{3} d u

Integral of a constant:

\int a d x = a x

= (- \frac{2}{3}) u

Substitute back

u = 5 - x^{3}

= (- \frac{2}{3}) 5 - x^{3}

Simplify

= - \frac{2}{3} 5 - x^{3}

Add a constant to the solution

= - \frac{2}{3} 5 - x^{3} + C

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What is the integral of (x^2)/(sqrt(5-x^3)) ?
The integral of (x^2)/(sqrt(5-x^3)) is -2/3 sqrt(5-x^3)+C