What is the integral of (5x^4-3x^6-8x^9)/(x^2) ?

The integral of (5x^4-3x^6-8x^9)/(x^2) is (5x^3)/3-(3x^5)/5-x^8+C

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integral of (5x^4-3x^6-8x^9)/(x^2)

\int \frac{5 x ^{4} - 3 x ^{6} - 8 x ^{9}}{x ^{2}} d x

\frac{5 x ^{3}}{3} - \frac{3 x ^{5}}{5} - x^{8} + C

Solution steps

\int \frac{5 x ^{4} - 3 x ^{6} - 8 x ^{9}}{x ^{2}} d x

Expand

\frac{5 x ^{4} - 3 x ^{6} - 8 x ^{9}}{x ^{2}} : \frac{5 x ^{4}}{x ^{2}} - \frac{3 x ^{6}}{x ^{2}} - \frac{8 x ^{9}}{x ^{2}}

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}}{x ^{2}} d x - \int \frac{3 x ^{6}}{x ^{2}} d x - \int \frac{8 x ^{9}}{x ^{2}} d x

\int \frac{5 x ^{4}}{x ^{2}} d x = \frac{5 x ^{3}}{3}

\int \frac{3 x ^{6}}{x ^{2}} d x = \frac{3 x ^{5}}{5}

\int \frac{8 x ^{9}}{x ^{2}} d x = x^{8}

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

Add a constant to the solution

= \frac{5 x ^{3}}{3} - \frac{3 x ^{5}}{5} - x^{8} + C

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What is the integral of (5x^4-3x^6-8x^9)/(x^2) ?
The integral of (5x^4-3x^6-8x^9)/(x^2) is (5x^3)/3-(3x^5)/5-x^8+C