What is the integral of x^4(7-(x^5)/(10))^3 ?

The integral of x^4(7-(x^5)/(10))^3 is -1/20000 (70-x^5)^4+C

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integral of x^4(7-(x^5)/(10))^3

\int x^{4} (7 - \frac{x ^{5}}{10})^{3} d x

- \frac{1}{20000} (70 - x^{5})^{4} + C

Solution steps

\int x^{4} (7 - \frac{x ^{5}}{10})^{3} d x

Apply u-substitution

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

Take the constant out:

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

= - 2 \cdot \int u^{3} d u

Apply the Power Rule

= - 2 \cdot \frac{u ^{4}}{4}

Substitute back

u = 7 - \frac{x ^{5}}{10}

= - 2 \cdot \frac{( 7 - \frac{x ^{5}}{10} ) ^{4}}{4}

Simplify

- 2 \cdot \frac{( 7 - \frac{x ^{5}}{10} ) ^{4}}{4} : - \frac{1}{20000} (70 - x^{5})^{4}

= - \frac{1}{20000} (70 - x^{5})^{4}

Add a constant to the solution

= - \frac{1}{20000} (70 - x^{5})^{4} + C

What is the integral of x^4(7-(x^5)/(10))^3 ?
The integral of x^4(7-(x^5)/(10))^3 is -1/20000 (70-x^5)^4+C