What is the integral of (x^2)/(sqrt(9+x^3)) ?

The integral of (x^2)/(sqrt(9+x^3)) is 2/3 sqrt(9+x^3)+C

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integral of (x^2)/(sqrt(9+x^3))

\int \frac{x ^{2}}{9 + x ^{3}} d x

\frac{2}{3} 9 + x^{3} + C

Solution steps

\int \frac{x ^{2}}{9 + 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 = 9 + x^{3}

= \frac{2}{3} 9 + x^{3}

Add a constant to the solution

= \frac{2}{3} 9 + x^{3} + C

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What is the integral of (x^2)/(sqrt(9+x^3)) ?
The integral of (x^2)/(sqrt(9+x^3)) is 2/3 sqrt(9+x^3)+C