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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{1}^{2} 4^{- θ} d θ

f (x) = 2 (2)^{4} - 16 (2)^{3} + 8

y^{^{'}} = - y + sin (x) + cos (x)

f (x) = 3 x + 2 z + 4 x z

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

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