What is the integral of (4x^{-3}-5x^{-2}+1) ?

The integral of (4x^{-3}-5x^{-2}+1) is -2/(x^2)+5/x+x+C

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integral of (4x^{-3}-5x^{-2}+1)

\int (4 x^{- 3} - 5 x^{- 2} + 1) d x

- \frac{2}{x ^{2}} + \frac{5}{x} + x + C

Solution steps

\int 4 x^{- 3} - 5 x^{- 2} + 1 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 4 x^{- 3} d x - \int 5 x^{- 2} d x + \int 1 d x

\int 4 x^{- 3} d x = - \frac{2}{x ^{2}}

\int 5 x^{- 2} d x = - \frac{5}{x}

\int 1 d x = x

= - \frac{2}{x ^{2}} - (- \frac{5}{x}) + x

Simplify

= - \frac{2}{x ^{2}} + \frac{5}{x} + x

Add a constant to the solution

= - \frac{2}{x ^{2}} + \frac{5}{x} + x + C

What is the integral of (4x^{-3}-5x^{-2}+1) ?
The integral of (4x^{-3}-5x^{-2}+1) is -2/(x^2)+5/x+x+C