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Identical expressions
x^(- two)((- one)^ two + two)^(- one / two)
x to the power of ( minus 2)(( minus 1) squared plus 2) to the power of ( minus 1 divide by 2)
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x to the power of (-2)((-1) to the power of 2+2) to the power of (-1/2)
x^-2-1^2+2^-1/2
x^(-2)((-1)^2+2)^(-1 divide by 2)
x^(-2)((-1)^2+2)^(-1/2)dx
Similar expressions
x^(-2)((-1)^2+2)^(1/2)
x^(2)((-1)^2+2)^(-1/2)
x^(-2)((-1)^2-2)^(-1/2)
x^(-2)((1)^2+2)^(-1/2)

Solving integrals/ x^(-2)((-1)^2+2)^(-1/2)

Integral of x^(-2)((-1)^2+2)^(-1/2) dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |          1           
 |  ----------------- dx
 |        ___________   
 |   2   /     2        
 |  x *\/  (-1)  + 2    
 |                      
/                       
0

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

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

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{1}{x^{2} \sqrt{\left(-1\right)^{2} + 2}}\, dx = \frac{\int \frac{1}{x^{2}}\, dx}{\sqrt{\left(-1\right)^{2} + 2}}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
So, the result is: $- \frac{1}{x \sqrt{\left(-1\right)^{2} + 2}}$
Now simplify:

$- \frac{\sqrt{3}}{3 x}$
Add the constant of integration:

$- \frac{\sqrt{3}}{3 x}+ \mathrm{constant}$

The answer is:

$- \frac{\sqrt{3}}{3 x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                            
 |         1                         1        
 | ----------------- dx = C - ----------------
 |       ___________               ___________
 |  2   /     2                   /     2     
 | x *\/  (-1)  + 2           x*\/  (-1)  + 2 
 |                                            
/

$$-{{1}\over{\sqrt{3}\,x}}$$

Simplify

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Plot the graph f(x)

The answer [src]

oo

$${\it \%a}$$

oo

$$\infty$$

Упростить

Numerical answer [src]

7.96352896763247e+18

7.96352896763247e+18

The graph

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

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Identical expressions

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Integral of x^(-2)((-1)^2+2)^(-1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution