What is the integral of (1-x)^{10} ?

The integral of (1-x)^{10} is -((1-x)^{11})/(11)+C

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integral of (1-x)^{10}

\int (1 - x)^{10} d x

- \frac{( 1 - x ) ^{11}}{11} + C

Solution steps

\int (1 - x)^{10} d x

Apply u-substitution

= \int - u^{10} d u

Take the constant out:

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

= - \int u^{10} d u

Apply the Power Rule

= - \frac{u ^{11}}{11}

Substitute back

u = 1 - x

= - \frac{( 1 - x ) ^{11}}{11}

Add a constant to the solution

= - \frac{( 1 - x ) ^{11}}{11} + C

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What is the integral of (1-x)^{10} ?
The integral of (1-x)^{10} is -((1-x)^{11})/(11)+C