What is the integral of (4x^3-5sqrt(x))/x ?

The integral of (4x^3-5sqrt(x))/x is (4x^3)/3-10sqrt(x)+C

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integral of (4x^3-5sqrt(x))/x

\int \frac{4 x ^{3} - 5 x}{x} d x

\frac{4 x ^{3}}{3} - 10 x + C

Solution steps

\int \frac{4 x ^{3} - 5 x}{x} d x

Expand

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

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

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

\int \frac{5}{x} d x = 10 x

= \frac{4 x ^{3}}{3} - 10 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} - 10 x + C

\frac{\partial}{\partial x} (\frac{r}{x})

\int \frac{1}{x ^{2} 64 x ^{2} + 81} d x

\frac{d y}{d x} = \frac{( x - 1 )}{y - 4}

y = \frac{1}{2} x + 8

f^{^{'}} (x) = x

What is the integral of (4x^3-5sqrt(x))/x ?
The integral of (4x^3-5sqrt(x))/x is (4x^3)/3-10sqrt(x)+C