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Popular >

integral of 8x^{-3}

Solution

\int 8 x^{- 3} d x

Solution

- \frac{4}{x ^{2}} + C

Solution steps

\int 8 x^{- 3} d x

Take the constant out:

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

= 8 \cdot \int x^{- 3} d x

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

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

Simplify

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

= - \frac{4}{x ^{2}}

Add a constant to the solution

= - \frac{4}{x ^{2}} + C

Popular Examples

integral from 0 to 2 of e^{-x}

\int_{0}^{2} e^{- x} d x

integral of sqrt(3+x^2)

\int 3 + x^{2} d x

integral of (3x^2-9x+2)

\int (3 x^{2} - 9 x + 2) d x

derivative of sqrt(3x+9)

\frac{d}{d x} (3 x + 9)

integral of sqrt((1+cos(x))/(1-cos(x)))

\int \frac{1 + cos ( x )}{1 - cos ( x )} d x

Frequently Asked Questions (FAQ)

What is the integral of 8x^{-3} ?
The integral of 8x^{-3} is -4/(x^2)+C