What is the integral of (9-2x)^{12} ?

The integral of (9-2x)^{12} is -1/26 (9-2x)^{13}+C

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integral of (9-2x)^{12}

\int (9 - 2 x)^{12} d x

- \frac{1}{26} (9 - 2 x)^{13} + C

Solution steps

\int (9 - 2 x)^{12} d x

Apply u-substitution

: \int - \frac{u ^{12}}{2} d u

= \int - \frac{u ^{12}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int u^{12} d u

Apply the Power Rule

: \frac{u ^{13}}{13}

= - \frac{1}{2} \cdot \frac{u ^{13}}{13}

Substitute back

u = 9 - 2 x

= - \frac{1}{2} \cdot \frac{( 9 - 2 x ) ^{13}}{13}

Simplify

- \frac{1}{2} \cdot \frac{( 9 - 2 x ) ^{13}}{13} : - \frac{1}{26} (9 - 2 x)^{13}

= - \frac{1}{26} (9 - 2 x)^{13}

Add a constant to the solution

= - \frac{1}{26} (9 - 2 x)^{13} + C

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What is the integral of (9-2x)^{12} ?
The integral of (9-2x)^{12} is -1/26 (9-2x)^{13}+C