What is the integral of (5x^3-8)/(x^3) ?

The integral of (5x^3-8)/(x^3) is 5x+4/(x^2)+C

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integral of (5x^3-8)/(x^3)

\int \frac{5 x ^{3} - 8}{x ^{3}} d x

5 x + \frac{4}{x ^{2}} + C

Solution steps

\int \frac{5 x ^{3} - 8}{x ^{3}} d x

Expand

\frac{5 x ^{3} - 8}{x ^{3}} : 5 - \frac{8}{x ^{3}}

= \int 5 - \frac{8}{x ^{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 5 d x - \int \frac{8}{x ^{3}} d x

\int 5 d x = 5 x

\int \frac{8}{x ^{3}} d x = - \frac{4}{x ^{2}}

= 5 x - (- \frac{4}{x ^{2}})

Simplify

= 5 x + \frac{4}{x ^{2}}

Add a constant to the solution

= 5 x + \frac{4}{x ^{2}} + C

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What is the integral of (5x^3-8)/(x^3) ?
The integral of (5x^3-8)/(x^3) is 5x+4/(x^2)+C