What is the integral of (1-5y)^3 ?

The integral of (1-5y)^3 is -1/20 (1-5y)^4+C

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integral of (1-5y)^3

\int (1 - 5 y)^{3} d y

- \frac{1}{20} (1 - 5 y)^{4} + C

Solution steps

\int (1 - 5 y)^{3} d y

Apply u-substitution

: \int - \frac{u ^{3}}{5} d u

= \int - \frac{u ^{3}}{5} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{1}{5} \cdot \frac{u ^{4}}{4}

Substitute back

u = 1 - 5 y

= - \frac{1}{5} \cdot \frac{( 1 - 5 y ) ^{4}}{4}

Simplify

- \frac{1}{5} \cdot \frac{( 1 - 5 y ) ^{4}}{4} : - \frac{1}{20} (1 - 5 y)^{4}

= - \frac{1}{20} (1 - 5 y)^{4}

Add a constant to the solution

= - \frac{1}{20} (1 - 5 y)^{4} + C

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