What is the integral of x^2(3-10x^3)^4 ?

The integral of x^2(3-10x^3)^4 is -1/150 (3-10x^3)^5+C

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integral of x^2(3-10x^3)^4

\int x^{2} (3 - 10 x^{3})^{4} d x

- \frac{1}{150} (3 - 10 x^{3})^{5} + C

Solution steps

\int x^{2} (3 - 10 x^{3})^{4} d x

Apply u-substitution

: \int - \frac{u ^{4}}{30} d u

= \int - \frac{u ^{4}}{30} d u

Take the constant out:

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

= - \frac{1}{30} \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= - \frac{1}{30} \cdot \frac{u ^{5}}{5}

Substitute back

u = 3 - 10 x^{3}

= - \frac{1}{30} \cdot \frac{( 3 - 10 x ^{3} ) ^{5}}{5}

Simplify

- \frac{1}{30} \cdot \frac{( 3 - 10 x ^{3} ) ^{5}}{5} : - \frac{1}{150} (3 - 10 x^{3})^{5}

= - \frac{1}{150} (3 - 10 x^{3})^{5}

Add a constant to the solution

= - \frac{1}{150} (3 - 10 x^{3})^{5} + C

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What is the integral of x^2(3-10x^3)^4 ?
The integral of x^2(3-10x^3)^4 is -1/150 (3-10x^3)^5+C