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

The integral of (8x-6)^5 is 1/48 (8x-6)^6+C

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integral of (8x-6)^5

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

\frac{1}{48} (8 x - 6)^{6} + C

Solution steps

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

Apply u-substitution

: \int \frac{u ^{5}}{8} d u

= \int \frac{u ^{5}}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{8} \cdot \frac{u ^{6}}{6}

Substitute back

u = 8 x - 6

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

Simplify

\frac{1}{8} \cdot \frac{( 8 x - 6 ) ^{6}}{6} : \frac{1}{48} (8 x - 6)^{6}

= \frac{1}{48} (8 x - 6)^{6}

Add a constant to the solution

= \frac{1}{48} (8 x - 6)^{6} + C

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