What is the integral of (6x-8)^5 ?

The integral of (6x-8)^5 is 1/36 (6x-8)^6+C

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integral of (6x-8)^5

\int (6 x - 8)^{5} d x

\frac{1}{36} (6 x - 8)^{6} + C

Solution steps

\int (6 x - 8)^{5} d x

Apply u-substitution

= \int \frac{u ^{5}}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int u^{5} d u

Apply the Power Rule

= \frac{1}{6} \cdot \frac{u ^{6}}{6}

Substitute back

u = 6 x - 8

= \frac{1}{6} \cdot \frac{( 6 x - 8 ) ^{6}}{6}

Simplify

\frac{1}{6} \cdot \frac{( 6 x - 8 ) ^{6}}{6} : \frac{1}{36} (6 x - 8)^{6}

= \frac{1}{36} (6 x - 8)^{6}

Add a constant to the solution

= \frac{1}{36} (6 x - 8)^{6} + C