What is the integral of (5-2x)^{21} ?

The integral of (5-2x)^{21} is -1/44 (5-2x)^{22}+C

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integral of (5-2x)^{21}

\int (5 - 2 x)^{21} d x

- \frac{1}{44} (5 - 2 x)^{22} + C

Solution steps

\int (5 - 2 x)^{21} d x

Apply u-substitution

: \int - \frac{u ^{21}}{2} d u

= \int - \frac{u ^{21}}{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^{21} d u

Apply the Power Rule

: \frac{u ^{22}}{22}

= - \frac{1}{2} \cdot \frac{u ^{22}}{22}

Substitute back

u = 5 - 2 x

= - \frac{1}{2} \cdot \frac{( 5 - 2 x ) ^{22}}{22}

Simplify

- \frac{1}{2} \cdot \frac{( 5 - 2 x ) ^{22}}{22} : - \frac{1}{44} (5 - 2 x)^{22}

= - \frac{1}{44} (5 - 2 x)^{22}

Add a constant to the solution

= - \frac{1}{44} (5 - 2 x)^{22} + C

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What is the integral of (5-2x)^{21} ?
The integral of (5-2x)^{21} is -1/44 (5-2x)^{22}+C