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Identical expressions
sqrt(x^ two - eight)/x^ four
square root of (x squared minus 8) divide by x to the power of 4
square root of (x to the power of two minus eight) divide by x to the power of four
√(x^2-8)/x^4
sqrt(x2-8)/x4
sqrtx2-8/x4
sqrt(x²-8)/x⁴
sqrt(x to the power of 2-8)/x to the power of 4
sqrtx^2-8/x^4
sqrt(x^2-8) divide by x^4
sqrt(x^2-8)/x^4dx
Similar expressions
sqrt(x^2+8)/x^4

Solving integrals/ sqrt(x^2-8)/x^4

Integral of sqrt(x^2-8)/x^4 dx

The solution

You have entered [src]

     ___              
 2*\/ 2               
    /                 
   |                  
   |       ________   
   |      /  2        
   |    \/  x  - 8    
   |    ----------- dx
   |          4       
   |         x        
   |                  
  /                   
    ___               
4*\/ 6                
-------               
   3

$$\int\limits_{\frac{4 \sqrt{6}}{3}}^{2 \sqrt{2}} \frac{\sqrt{x^{2} - 8}}{x^{4}}\, dx$$

Integral(sqrt(x^2 - 8)/x^4, (x, 4*sqrt(6)/3, 2*sqrt(2)))

Detail solution

TrigSubstitutionRule(theta=_theta, func=2*sqrt(2)*sec(_theta), rewritten=sin(_theta)**2*cos(_theta)/8, substep=ConstantTimesRule(constant=1/8, other=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), context=sin(_theta)**2*cos(_theta)/8, symbol=_theta), restriction=(x > -2*sqrt(2)) & (x < 2*sqrt(2)), context=sqrt(x**2 - 8)/x**4, symbol=x)

Add the constant of integration:

$\begin{cases} \frac{\left(x^{2} - 8\right)^{\frac{3}{2}}}{24 x^{3}} & \text{for}\: x > - 2 \sqrt{2} \wedge x < 2 \sqrt{2} \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} \frac{\left(x^{2} - 8\right)^{\frac{3}{2}}}{24 x^{3}} & \text{for}\: x > - 2 \sqrt{2} \wedge x < 2 \sqrt{2} \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                        
 |                                                                         
 |    ________          //         3/2                                    \
 |   /  2               ||/      2\                                       |
 | \/  x  - 8           ||\-8 + x /            /         ___          ___\|
 | ----------- dx = C + |<------------  for And\x > -2*\/ 2 , x < 2*\/ 2 /|
 |       4              ||       3                                        |
 |      x               ||   24*x                                         |
 |                      \\                                                /
/

$$\int \frac{\sqrt{x^{2} - 8}}{x^{4}}\, dx = C + \begin{cases} \frac{\left(x^{2} - 8\right)^{\frac{3}{2}}}{24 x^{3}} & \text{for}\: x > - 2 \sqrt{2} \wedge x < 2 \sqrt{2} \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/192

$$- \frac{1}{192}$$

-1/192

$$- \frac{1}{192}$$

-1/192

Numerical answer [src]

-0.00520833333333333

-0.00520833333333333

The graph

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

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Integral of sqrt(x^2-8)/x^4 dx

Limits of integration:

The graph:

Piecewise:

The solution