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

The integral of (5x^3-3sqrt(x))/x is (5x^3)/3-6sqrt(x)+C

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

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

\frac{5 x ^{3}}{3} - 6 x + C

Solution steps

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

Expand

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

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

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

\int \frac{3}{x} d x = 6 x

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

Add a constant to the solution

= \frac{5 x ^{3}}{3} - 6 x + C

\int_{22}^{4} \frac{1}{t ^{3} t ^{2} - 4} d t

y^{^{'}} + y cos (x) = 0

x + 1

\int_{1}^{2} \frac{x ^{2} + 8}{3 x - x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 1})

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