What is the integral of 10(x-6)^4 ?

The integral of 10(x-6)^4 is 2(x-6)^5+C

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integral of 10(x-6)^4

\int 10 (x - 6)^{4} d x

2 (x - 6)^{5} + C

Solution steps

\int 10 (x - 6)^{4} d x

Take the constant out:

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

= 10 \cdot \int (x - 6)^{4} d x

Apply u-substitution

: \int u^{4} d u

= 10 \cdot \int u^{4} d u

Apply the Power Rule

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

= 10 \cdot \frac{u ^{5}}{5}

Substitute back

u = x - 6

= 10 \cdot \frac{( x - 6 ) ^{5}}{5}

Simplify

10 \cdot \frac{( x - 6 ) ^{5}}{5} : 2 (x - 6)^{5}

= 2 (x - 6)^{5}

Add a constant to the solution

= 2 (x - 6)^{5} + C

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