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Popular >

integral of 12x^{-3}

Solution

\int 12 x^{- 3} d x

Solution

- \frac{6}{x ^{2}} + C

Solution steps

\int 12 x^{- 3} d x

Take the constant out:

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

= 12 \cdot \int x^{- 3} d x

Apply the Power Rule

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

= 12 (- \frac{1}{2 x ^{2}})

Simplify

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

= - \frac{6}{x ^{2}}

Add a constant to the solution

= - \frac{6}{x ^{2}} + C

Popular Examples

integral of x^3sqrt(6+x^4)

\int x^{3} 6 + x^{4} d x

integral of x^2sqrt(x^3-27)

\int x^{2} x^{3} - 27 d x

integral of (x^3-3x^2+4x-1)/(3x)

\int \frac{x ^{3} - 3 x ^{2} + 4 x - 1}{3 x} d x

integral of (x^3+2)^2

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

integral of (2xsqrt(x)-5x-2)

\int (2 x x - 5 x - 2) d x

Frequently Asked Questions (FAQ)

What is the integral of 12x^{-3} ?
The integral of 12x^{-3} is -6/(x^2)+C