What is the integral of (3x^2-5sqrt(x))/x ?

The integral of (3x^2-5sqrt(x))/x is (3x^2)/2-10sqrt(x)+C

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integral of (3x^2-5sqrt(x))/x

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

\frac{3 x ^{2}}{2} - 10 x + C

Solution steps

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

Expand

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

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

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

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

= \frac{3 x ^{2}}{2} - 10 x

Add a constant to the solution

= \frac{3 x ^{2}}{2} - 10 x + C

x \to \infty lim (2 + \frac{1}{x})

y = x sin (2 x)

\int \frac{12}{1 - cos ( 2 x )} d x

\int_{1}^{4} - 7 x ln (x) d x

\int \frac{4 x}{( 3 x ^{2} - 1 ) ^{5}} d x

What is the integral of (3x^2-5sqrt(x))/x ?
The integral of (3x^2-5sqrt(x))/x is (3x^2)/2-10sqrt(x)+C