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Identical expressions
(x^ two -2x+ three)/(xcqrtx)
(x squared minus 2x plus 3) divide by (xcqrtx)
(x to the power of two minus 2x plus three) divide by (xcqrtx)
(x2-2x+3)/(xcqrtx)
x2-2x+3/xcqrtx
(x²-2x+3)/(xcqrtx)
(x to the power of 2-2x+3)/(xcqrtx)
x^2-2x+3/xcqrtx
(x^2-2x+3) divide by (xcqrtx)
(x^2-2x+3)/(xcqrtx)dx
Similar expressions
(x^2-2x-3)/(xcqrtx)
(x^2+2x+3)/(xcqrtx)

Integral of (x^2-2x+3)/(xcqrtx) dx

The solution

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  1                
  /                
 |                 
 |   2             
 |  x  - 2*x + 3   
 |  ------------ dx
 |        ___      
 |    x*\/ x       
 |                 
/                  
0

$$\int\limits_{0}^{1} \frac{\left(x^{2} - 2 x\right) + 3}{\sqrt{x} x}\, dx$$

Integral((x^2 - 2*x + 3)/((x*sqrt(x))), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{\left(x^{2} - 2 x\right) + 3}{\sqrt{x} x} = \sqrt{x} - \frac{2}{\sqrt{x}} + \frac{3}{x^{\frac{3}{2}}}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{2}{\sqrt{x}}\right)\, dx = - 2 \int \frac{1}{\sqrt{x}}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{\sqrt{x}}\, dx = 2 \sqrt{x}$
  So, the result is: $- 4 \sqrt{x}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3}{x^{\frac{3}{2}}}\, dx = 3 \int \frac{1}{x^{\frac{3}{2}}}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{x^{\frac{3}{2}}}\, dx = - \frac{2}{\sqrt{x}}$
  So, the result is: $- \frac{6}{\sqrt{x}}$
The result is: $\frac{2 x^{\frac{3}{2}}}{3} - 4 \sqrt{x} - \frac{6}{\sqrt{x}}$
Now simplify:

$\frac{2 \left(x \left(x - 6\right) - 9\right)}{3 \sqrt{x}}$
Add the constant of integration:

$\frac{2 \left(x \left(x - 6\right) - 9\right)}{3 \sqrt{x}}+ \mathrm{constant}$

The answer is:

$\frac{2 \left(x \left(x - 6\right) - 9\right)}{3 \sqrt{x}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 |  2                                         3/2
 | x  - 2*x + 3            6         ___   2*x   
 | ------------ dx = C - ----- - 4*\/ x  + ------
 |       ___               ___               3   
 |   x*\/ x              \/ x                    
 |                                               
/

$$\int \frac{\left(x^{2} - 2 x\right) + 3}{\sqrt{x} x}\, dx = C + \frac{2 x^{\frac{3}{2}}}{3} - 4 \sqrt{x} - \frac{6}{\sqrt{x}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

22393345789.6361

22393345789.6361

Use the examples entering the upper and lower limits of integration.

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Identical expressions

Similar expressions

Integral of (x^2-2x+3)/(xcqrtx) dx

Limits of integration:

The graph:

Piecewise:

The solution