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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

= - \frac{1}{x ^{2}} - \frac{3}{x} + 2 x + C

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Frequently Asked Questions (FAQ)

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