What is the integral of 14(x-5)^6 ?

The integral of 14(x-5)^6 is 2(x-5)^7+C

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integral of 14(x-5)^6

\int 14 (x - 5)^{6} d x

2 (x - 5)^{7} + C

Solution steps

\int 14 (x - 5)^{6} d x

Take the constant out:

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

= 14 \cdot \int (x - 5)^{6} d x

Apply u-substitution

: \int u^{6} d u

= 14 \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= 14 \cdot \frac{u ^{7}}{7}

Substitute back

u = x - 5

= 14 \cdot \frac{( x - 5 ) ^{7}}{7}

Simplify

14 \cdot \frac{( x - 5 ) ^{7}}{7} : 2 (x - 5)^{7}

= 2 (x - 5)^{7}

Add a constant to the solution

= 2 (x - 5)^{7} + C

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