What is the integral of 6(5-6x)^4 ?

The integral of 6(5-6x)^4 is -1/5 (5-6x)^5+C

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integral of 6(5-6x)^4

\int 6 (5 - 6 x)^{4} d x

- \frac{1}{5} (5 - 6 x)^{5} + C

Solution steps

\int 6 (5 - 6 x)^{4} d x

Take the constant out:

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

= 6 \cdot \int (5 - 6 x)^{4} d x

Apply u-substitution

: \int - \frac{u ^{4}}{6} d u

= 6 \cdot \int - \frac{u ^{4}}{6} d u

Take the constant out:

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

= 6 (- \frac{1}{6} \cdot \int u^{4} d u)

Apply the Power Rule

: \frac{u ^{5}}{5}

= 6 (- \frac{1}{6} \cdot \frac{u ^{5}}{5})

Substitute back

u = 5 - 6 x

= 6 (- \frac{1}{6} \cdot \frac{( 5 - 6 x ) ^{5}}{5})

Simplify

6 (- \frac{1}{6} \cdot \frac{( 5 - 6 x ) ^{5}}{5}) : - \frac{1}{5} (5 - 6 x)^{5}

= - \frac{1}{5} (5 - 6 x)^{5}

Add a constant to the solution

= - \frac{1}{5} (5 - 6 x)^{5} + C

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What is the integral of 6(5-6x)^4 ?
The integral of 6(5-6x)^4 is -1/5 (5-6x)^5+C