What is the integral of (2x-6)^3 ?

The integral of (2x-6)^3 is 1/8 (2x-6)^4+C

Popular >

integral of (2x-6)^3

\int (2 x - 6)^{3} d x

\frac{1}{8} (2 x - 6)^{4} + C

Solution steps

\int (2 x - 6)^{3} d x

Apply u-substitution

: \int \frac{u ^{3}}{2} d u

= \int \frac{u ^{3}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{1}{2} \cdot \frac{u ^{4}}{4}

Substitute back

u = 2 x - 6

= \frac{1}{2} \cdot \frac{( 2 x - 6 ) ^{4}}{4}

Simplify

\frac{1}{2} \cdot \frac{( 2 x - 6 ) ^{4}}{4} : \frac{1}{8} (2 x - 6)^{4}

= \frac{1}{8} (2 x - 6)^{4}

Add a constant to the solution

= \frac{1}{8} (2 x - 6)^{4} + C

\frac{d}{d x} (\frac{1}{1 + 4 x})

\int_{0}^{3} (x + 1)^{\frac{1}{2}} d x

\frac{\partial}{\partial x} (ln (5 y e^{x y}))

\int \frac{cos ( x )}{2 x} d x

\int \frac{e ^{x}}{49 - e ^{2 x}} d x