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

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

Popular >

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

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

\frac{2}{5} x^{\frac{5}{2}} - 2 x^{\frac{3}{2}} + C

Solution steps

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

Expand

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

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

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

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

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - 2 x^{\frac{3}{2}} + C

\int \frac{3 x + 1}{x ^{3} - 4 x ^{2} + x + 6} d x

\int (t - 1) (2 + t^{2}) d t

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

\int y \cdot cos (y) d y

\int 2 cos (x) sin (2 x) d x

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