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Popular >

integral of-2x^{-3}

Solution

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

Solution

\frac{1}{x ^{2}} + C

Solution steps

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

Take the constant out:

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

= - 2 \cdot \int x^{- 3} d x

Apply the Power Rule

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

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

Simplify

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

= \frac{1}{x ^{2}}

Add a constant to the solution

= \frac{1}{x ^{2}} + C

Popular Examples

area y^2=2x,x=2y area

y^{2} = 2 x, x = 2 y

x^2y^{''}+xy^'-4y=0

x^{2} y^{^{''}} + x y^{^{'}} - 4 y = 0

derivative of cos(x+cot(x)+csc(x)+3e^x)

\frac{d}{d x} (cos (x) + cot (x) + csc (x) + 3 e^{x})

sum from n=0 to infinity of (2/3)^{-n}

n = 0 \sum \infty (\frac{2}{3})^{- n}

derivative of f(x)=(7^x)/(x^3)derivative of

f (x) = \frac{7 ^{x}}{x ^{3}}

Frequently Asked Questions (FAQ)

What is the integral of-2x^{-3} ?
The integral of-2x^{-3} is 1/(x^2)+C