What is the integral of (5-3x)^{10} ?

The integral of (5-3x)^{10} is -1/33 (5-3x)^{11}+C

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integral of (5-3x)^{10}

\int (5 - 3 x)^{10} d x

- \frac{1}{33} (5 - 3 x)^{11} + C

Solution steps

\int (5 - 3 x)^{10} d x

Apply u-substitution

: \int - \frac{u ^{10}}{3} d u

= \int - \frac{u ^{10}}{3} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= - \frac{1}{3} \cdot \frac{u ^{11}}{11}

Substitute back

u = 5 - 3 x

= - \frac{1}{3} \cdot \frac{( 5 - 3 x ) ^{11}}{11}

Simplify

- \frac{1}{3} \cdot \frac{( 5 - 3 x ) ^{11}}{11} : - \frac{1}{33} (5 - 3 x)^{11}

= - \frac{1}{33} (5 - 3 x)^{11}

Add a constant to the solution

= - \frac{1}{33} (5 - 3 x)^{11} + C

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What is the integral of (5-3x)^{10} ?
The integral of (5-3x)^{10} is -1/33 (5-3x)^{11}+C