What is the integral of 6(x-12)^5 ?

The integral of 6(x-12)^5 is (x-12)^6+C

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integral of 6(x-12)^5

\int 6 (x - 12)^{5} d x

(x - 12)^{6} + C

Solution steps

\int 6 (x - 12)^{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 - 12)^{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 - 12

= 6 \cdot \frac{( x - 12 ) ^{6}}{6}

Simplify

6 \cdot \frac{( x - 12 ) ^{6}}{6} : (x - 12)^{6}

= (x - 12)^{6}

Add a constant to the solution

= (x - 12)^{6} + C

f (x) = x^{2} - 6, at x = 3

6 e^{z}

\int \frac{1}{x ( x - 7 )} d x

\frac{d}{d y} (\frac{1}{1 + y ^{2}})

\frac{\partial}{\partial v} (u + uv)