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Popular >

integral of 6(x-4)^5

Solution

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

Solution

(x - 4)^{6} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u^{5} d u

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

Apply the Power Rule

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

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

Substitute back

u = x - 4

= 6 \cdot \frac{( x - 4 ) ^{6}}{6}

Simplify

6 \cdot \frac{( x - 4 ) ^{6}}{6} : (x - 4)^{6}

= (x - 4)^{6}

Add a constant to the solution

= (x - 4)^{6} + C

Graph

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Frequently Asked Questions (FAQ)

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