What is the integral of (-1)/(x^3) ?

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

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integral of (-1)/(x^3)

integral

\frac{- 1}{x ^{3}}

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

Solution steps

\int \frac{- 1}{x ^{3}} d x

Take the constant out:

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

= - \int \frac{1}{x ^{3}} d x

Apply the Power Rule

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

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

Simplify

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

Add a constant to the solution

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

a + 3 c - 2 d

(1 - 0.1 x)^{- 2}

5 - (\frac{8}{x ^{2}})

2 x^{3} (e^{x})^{- 2}

x^{3} (a^{3} - x^{3})^{5}