What is the integral of x^{-3}+x^{-2} ?

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

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integral of x^{-3}+x^{-2}

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

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

Solution steps

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

Simplify

x^{- 3} + x^{- 2} : \frac{1}{x ^{3}} + \frac{1}{x ^{2}}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

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

Add a constant to the solution

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

1 + x

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\frac{\partial}{\partial y} ((x + y)^{3} - 12 x y)

\int x \cdot sin (2 x^{2}) d x

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