What is the integral of (3x-8)^{21} ?

The integral of (3x-8)^{21} is 1/66 (3x-8)^{22}+C

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integral of (3x-8)^{21}

\int (3 x - 8)^{21} d x

\frac{1}{66} (3 x - 8)^{22} + C

Solution steps

\int (3 x - 8)^{21} d x

Apply u-substitution

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

Apply the Power Rule

= \frac{1}{3} \cdot \frac{u ^{22}}{22}

Substitute back

u = 3 x - 8

= \frac{1}{3} \cdot \frac{( 3 x - 8 ) ^{22}}{22}

Simplify

\frac{1}{3} \cdot \frac{( 3 x - 8 ) ^{22}}{22} : \frac{1}{66} (3 x - 8)^{22}

= \frac{1}{66} (3 x - 8)^{22}

Add a constant to the solution

= \frac{1}{66} (3 x - 8)^{22} + C

What is the integral of (3x-8)^{21} ?
The integral of (3x-8)^{21} is 1/66 (3x-8)^{22}+C