What is the integral of (5x^4-10)/(x^6) ?

The integral of (5x^4-10)/(x^6) is -5/x+2/(x^5)+C

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integral of (5x^4-10)/(x^6)

\int \frac{5 x ^{4} - 10}{x ^{6}} d x

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

Solution steps

\int \frac{5 x ^{4} - 10}{x ^{6}} d x

Expand

\frac{5 x ^{4} - 10}{x ^{6}} : \frac{5}{x ^{2}} - \frac{10}{x ^{6}}

= \int \frac{5}{x ^{2}} - \frac{10}{x ^{6}} 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 ^{2}} d x - \int \frac{10}{x ^{6}} d x

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

\int \frac{10}{x ^{6}} d x = - \frac{2}{x ^{5}}

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

Simplify

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

Add a constant to the solution

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

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What is the integral of (5x^4-10)/(x^6) ?
The integral of (5x^4-10)/(x^6) is -5/x+2/(x^5)+C