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)

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

\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

\int_{- 2}^{2} \frac{1}{x ^{2}} d x

\int 2 e^{x} + 2 x - 1 d x

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x + x^{3} y^{2} d y = 0

\frac{\partial}{\partial y} (ln (x^{4} + y) - z)

\frac{16}{( x ^{2} y ^{2} )}