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

Integral of 1/(x^2sqrt(1+x^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 *\/  1 + x     
 |                     
/                      
0
∫011⋅1x2x2+1 dx\int\limits_{0}^{1} 1 \cdot \frac{1}{x^{2} \sqrt{x^{2} + 1}}\, dx
Simplify
Detail solution

    TrigSubstitutionRule(theta=_theta, func=tan(_theta), rewritten=cos(_theta)/sin(_theta)**2, substep=URule(u_var=_u, u_func=sin(_theta), constant=1, substep=PowerRule(base=_u, exp=-2, context=_u**(-2), symbol=_u), context=cos(_theta)/sin(_theta)**2, symbol=_theta), restriction=True, context=1/(x**2*sqrt(x**2 + 1)), symbol=x)

  1. Add the constant of integration:

    −x2+1x+constant- \frac{\sqrt{x^{2} + 1}}{x}+ \mathrm{constant}

The answer is:

−x2+1x+constant- \frac{\sqrt{x^{2} + 1}}{x}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             ________
 |                             /      2 
 |         1                 \/  1 + x  
 | 1*-------------- dx = C - -----------
 |         ________               x     
 |    2   /      2                      
 |   x *\/  1 + x                       
 |                                      
/
−x2+1x-{{\sqrt{x^2+1}}\over{x}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90200000000-100000000
Plot the graph f(x)
The answer [src] 
oo
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=
= 
oo
∞\infty
Simplify
Numerical answer [src] 
1.3793236779486e+19
1.3793236779486e+19
The graph
Integral of 1/(x^2sqrt(1+x^2)) dx

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

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