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

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

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

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

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

Solution steps

\int 5 x^{- 4} - 3 d x

5 x^{- 4} = \frac{5}{x ^{4}}

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

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

\int 3 d x = 3 x

= - \frac{5}{3 x ^{3}} - 3 x

Add a constant to the solution

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

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