What is the integral of (5x^2)/(sqrt(4-x^3)) ?

The integral of (5x^2)/(sqrt(4-x^3)) is -10/3 sqrt(4-x^3)+C

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integral of (5x^2)/(sqrt(4-x^3))

\int \frac{5 x ^{2}}{4 - x ^{3}} d x

- \frac{10}{3} 4 - x^{3} + C

Solution steps

\int \frac{5 x ^{2}}{4 - x ^{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{x ^{2}}{4 - x ^{3}} d x

Apply u-substitution

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

= 5 \cdot \int - \frac{2}{3} d u

Integral of a constant:

\int a d x = a x

= 5 (- \frac{2}{3}) u

Substitute back

u = 4 - x^{3}

= 5 (- \frac{2}{3}) 4 - x^{3}

Simplify

5 (- \frac{2}{3}) 4 - x^{3} : - \frac{10}{3} 4 - x^{3}

= - \frac{10}{3} 4 - x^{3}

Add a constant to the solution

= - \frac{10}{3} 4 - x^{3} + C

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What is the integral of (5x^2)/(sqrt(4-x^3)) ?
The integral of (5x^2)/(sqrt(4-x^3)) is -10/3 sqrt(4-x^3)+C