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1/(x^2(x^2-9)^(1/2))

  • How to use it?

  • Integral of d{x}:
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  • Integral of e^(2*x)/2 Integral of e^(2*x)/2
  • Integral of e^(x*(-5)) Integral of e^(x*(-5))
  • Integral of cos(x)^6 Integral of cos(x)^6

  • Identical expressions

  • one /(x^ two (x^ two - nine)^(one / two))
  • 1 divide by (x squared (x squared minus 9) to the power of (1 divide by 2))
  • one divide by (x to the power of two (x to the power of two minus nine) to the power of (one divide by two))
  • 1/(x2(x2-9)(1/2))
  • 1/x2x2-91/2
  • 1/(x²(x²-9)^(1/2))
  • 1/(x to the power of 2(x to the power of 2-9) to the power of (1/2))
  • 1/x^2x^2-9^1/2
  • 1 divide by (x^2(x^2-9)^(1 divide by 2))
  • 1/(x^2(x^2-9)^(1/2))dx

  • Similar expressions

  • 1/(x^2(x^2+9)^(1/2))
Solving integrals/ 1/(x^2(x^2-9)^(1/2))

Integral of 1/(x^2(x^2-9)^(1/2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |          1          
 |  1*-------------- dx
 |          ________   
 |     2   /  2        
 |    x *\/  x  - 9    
 |                     
/                      
0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x^{2} \sqrt{x^{2} - 9}}\, dx$$ 
Integral(1/(x^2*sqrt(x^2 - 1*9)), (x, 0, 1))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=3*sec(_theta), rewritten=cos(_theta)/9, substep=ConstantTimesRule(constant=1/9, other=cos(_theta), substep=TrigRule(func='cos', arg=_theta, context=cos(_theta), symbol=_theta), context=cos(_theta)/9, symbol=_theta), restriction=(x > -3) & (x < 3), context=1/(x**2*sqrt(x**2 - 1*9)), symbol=x)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                 
 |                           //   _________                        \
 |         1                 ||  /       2                         |
 | 1*-------------- dx = C + |<\/  -9 + x                          |
 |         ________          ||------------  for And(x > -3, x < 3)|
 |    2   /  2               \\    9*x                             /
 |   x *\/  x  - 9                                                  
 |                                                                  
/
$${{\sqrt{x^2-9}}\over{9\,x}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              ___
        2*I*\/ 2 
-oo*I + ---------
            9
$$\int_{0}^{1}{{{1}\over{x^2\,\sqrt{x^2-9}}}\;dx}$$ 
=
= 
              ___
        2*I*\/ 2 
-oo*I + ---------
            9
$$- \infty i + \frac{2 \sqrt{2} i}{9}$$
Упростить
Numerical answer [src] 
(0.0 - 4.59774559316199e+18j)
(0.0 - 4.59774559316199e+18j)
The graph
Integral of 1/(x^2(x^2-9)^(1/2)) dx

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

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