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Popular Calculus >

integral of 6x^{-3}

Solution

\int 6 x^{- 3} d x

Solution

- \frac{3}{x ^{2}} + C

Solution steps

\int 6 x^{- 3} d x

Take the constant out:

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

= 6 \cdot \int x^{- 3} d x

Apply the Power Rule

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

Simplify

6 (- \frac{1}{2 x ^{2}}) : - \frac{3}{x ^{2}}

= - \frac{3}{x ^{2}}

Add a constant to the solution

= - \frac{3}{x ^{2}} + C

Graph

Popular Examples

integral of (x^2+1)x

\int (x^{2} + 1) x d x

derivative of y=(2x^3+7)^2

d er i v a t i v e y = (2 x^{3} + 7)^{2}

area x^3,x^{1/3},[0,2]

a re a x^{3}, x^{\frac{1}{3}}, [0, 2]

derivative of (x-1/(x+3))

\frac{d}{d x} (\frac{x - 1}{x + 3})

integral of sin(2pix)

\int sin (2 π x) d x

Frequently Asked Questions (FAQ)

What is the integral of 6x^{-3} ?
The integral of 6x^{-3} is -3/(x^2)+C