What is the integral of (-10x^4-2x^{-3}+15x^{-4}) ?

The integral of (-10x^4-2x^{-3}+15x^{-4}) is -2x^5+1/(x^2)-5/(x^3)+C

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integral of (-10x^4-2x^{-3}+15x^{-4})

\int (- 10 x^{4} - 2 x^{- 3} + 15 x^{- 4}) d x

- 2 x^{5} + \frac{1}{x ^{2}} - \frac{5}{x ^{3}} + C

Solution steps

\int - 10 x^{4} - 2 x^{- 3} + 15 x^{- 4} 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 10 x^{4} d x - \int 2 x^{- 3} d x + \int 15 x^{- 4} d x

\int 10 x^{4} d x = 2 x^{5}

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

\int 15 x^{- 4} d x = - \frac{5}{x ^{3}}

= - 2 x^{5} - (- \frac{1}{x ^{2}}) - \frac{5}{x ^{3}}

Simplify

= - 2 x^{5} + \frac{1}{x ^{2}} - \frac{5}{x ^{3}}

Add a constant to the solution

= - 2 x^{5} + \frac{1}{x ^{2}} - \frac{5}{x ^{3}} + C

What is the integral of (-10x^4-2x^{-3}+15x^{-4}) ?
The integral of (-10x^4-2x^{-3}+15x^{-4}) is -2x^5+1/(x^2)-5/(x^3)+C