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

The integral of (1-x)^5 is -((1-x)^6)/6+C

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integral of (1-x)^5

integral

(1 - x)^{5}

- \frac{( 1 - x ) ^{6}}{6} + C

Solution steps

\int (1 - x)^{5} d x

Apply u-substitution

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

= - \frac{u ^{6}}{6}

Substitute back

u = 1 - x

= - \frac{( 1 - x ) ^{6}}{6}

Add a constant to the solution

= - \frac{( 1 - x ) ^{6}}{6} + C