What is the integral of ((x+1)(x-2))/(sqrt(x)) ?

The integral of ((x+1)(x-2))/(sqrt(x)) is 2/5 x^{5/2}-2/3 x^{3/2}-4sqrt(x)+C

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integral of ((x+1)(x-2))/(sqrt(x))

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

\frac{2}{5} x^{\frac{5}{2}} - \frac{2}{3} x^{\frac{3}{2}} - 4 x + C

Solution steps

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

Expand

\frac{( x + 1 ) ( x - 2 )}{x} : x^{\frac{3}{2}} - x - \frac{2}{x}

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

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

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

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

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

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - \frac{2}{3} x^{\frac{3}{2}} - 4 x + C

\frac{\partial}{\partial y} (x^{2} y + y z^{3} + z^{5} x)

\frac{d}{d x} ((x + \frac{1}{x}) (x - \frac{1}{x}))

y^{^{''}} + 10 y^{^{'}} + 25 = 0

\int (\frac{100}{25 + ( 5 y ) ^{2}} + e^{4}) d y

What is the integral of ((x+1)(x-2))/(sqrt(x)) ?
The integral of ((x+1)(x-2))/(sqrt(x)) is 2/5 x^{5/2}-2/3 x^{3/2}-4sqrt(x)+C