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

The integral of (5x^3-8sqrt(x))/x is (5x^3)/3-16sqrt(x)+C

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

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

\frac{5 x ^{3}}{3} - 16 x + C

Solution steps

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

Expand

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

= \int 5 x^{2} - \frac{8}{x} 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 x^{2} d x - \int \frac{8}{x} d x

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

\int \frac{8}{x} d x = 16 x

= \frac{5 x ^{3}}{3} - 16 x

Add a constant to the solution

= \frac{5 x ^{3}}{3} - 16 x + C

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What is the integral of (5x^3-8sqrt(x))/x ?
The integral of (5x^3-8sqrt(x))/x is (5x^3)/3-16sqrt(x)+C