What is the integral of (5x-6x^7)/(x^4) ?

The integral of (5x-6x^7)/(x^4) is -5/(2x^2)-(3x^4)/2+C

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integral of (5x-6x^7)/(x^4)

\int \frac{5 x - 6 x ^{7}}{x ^{4}} d x

- \frac{5}{2 x ^{2}} - \frac{3 x ^{4}}{2} + C

Solution steps

\int \frac{5 x - 6 x ^{7}}{x ^{4}} d x

Simplify

\frac{5 x - 6 x ^{7}}{x ^{4}} : \frac{5 - 6 x ^{6}}{x ^{3}}

= \int \frac{5 - 6 x ^{6}}{x ^{3}} d x

Expand

\frac{5 - 6 x ^{6}}{x ^{3}} : \frac{5}{x ^{3}} - 6 x^{3}

= \int \frac{5}{x ^{3}} - 6 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 \frac{5}{x ^{3}} d x - \int 6 x^{3} d x

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

= - \frac{5}{2 x ^{2}} - \frac{3 x ^{4}}{2}

Add a constant to the solution

= - \frac{5}{2 x ^{2}} - \frac{3 x ^{4}}{2} + C

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What is the integral of (5x-6x^7)/(x^4) ?
The integral of (5x-6x^7)/(x^4) is -5/(2x^2)-(3x^4)/2+C