What is the integral of (a-x)^3 ?

The integral of (a-x)^3 is -((a-x)^4)/4+C

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integral of (a-x)^3

\int (a - x)^{3} d x

- \frac{( a - x ) ^{4}}{4} + C

Solution steps

\int (a - x)^{3} d x

Apply u-substitution

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

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

Substitute back

u = a - x

= - \frac{( a - x ) ^{4}}{4}

Add a constant to the solution

= - \frac{( a - x ) ^{4}}{4} + C