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  • Integral of d{x}:
  • Integral of cosx^2 Integral of cosx^2
  • Integral of sinh(x) Integral of sinh(x)
  • Integral of 2/x^4 Integral of 2/x^4
  • Integral of 1/(1+4x^2) Integral of 1/(1+4x^2)

  • Identical expressions

  • x^(- four)*sqrt((x^ two - one))
  • x to the power of ( minus 4) multiply by square root of ((x squared minus 1))
  • x to the power of ( minus four) multiply by square root of ((x to the power of two minus one))
  • x^(-4)*√((x^2-1))
  • x(-4)*sqrt((x2-1))
  • x-4*sqrtx2-1
  • x^(-4)*sqrt((x²-1))
  • x to the power of (-4)*sqrt((x to the power of 2-1))
  • x^(-4)sqrt((x^2-1))
  • x(-4)sqrt((x2-1))
  • x-4sqrtx2-1
  • x^-4sqrtx^2-1
  • x^(-4)*sqrt((x^2-1))dx

  • Similar expressions

  • x^(4)*sqrt((x^2-1))
  • x^(-4)*sqrt((x^2+1))
Solving integrals/ x^(-4)*sqrt((x^2-1))

Integral of x^(-4)*sqrt((x^2-1)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2               
  /               
 |                
 |     ________   
 |    /  2        
 |  \/  x  - 1    
 |  ----------- dx
 |        4       
 |       x        
 |                
/                 
1
$$\int\limits_{1}^{2} \frac{\sqrt{x^{2} - 1}}{x^{4}}\, dx$$ 
Integral(sqrt(x^2 - 1)/x^4, (x, 1, 2))
Detail solution

    TrigSubstitutionRule(theta=_theta, func=sec(_theta), rewritten=sin(_theta)**2*cos(_theta), substep=URule(u_var=_u, u_func=sin(_theta), constant=1, substep=PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), context=sin(_theta)**2*cos(_theta), symbol=_theta), restriction=(x > -1) & (x < 1), context=sqrt(x**2 - 1)/x**4, symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                            
 |                                                             
 |    ________          //         3/2                        \
 |   /  2               ||/      2\                           |
 | \/  x  - 1           ||\-1 + x /                           |
 | ----------- dx = C + |<------------  for And(x > -1, x < 1)|
 |       4              ||       3                            |
 |      x               ||    3*x                             |
 |                      \\                                    /
/
$$\int \frac{\sqrt{x^{2} - 1}}{x^{4}}\, dx = C + \begin{cases} \frac{\left(x^{2} - 1\right)^{\frac{3}{2}}}{3 x^{3}} & \text{for}\: x > -1 \wedge x < 1 \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___
\/ 3 
-----
  8
$$\frac{\sqrt{3}}{8}$$ 
=
= 
  ___
\/ 3 
-----
  8
$$\frac{\sqrt{3}}{8}$$ 
sqrt(3)/8
Numerical answer [src] 
0.21650635094611
0.21650635094611

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

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