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(x^2)/(1+x^6)

Integral of (x^2)/(1+x^6) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |     2     
 |    x      
 |  ------ dx
 |       6   
 |  1 + x    
 |           
/            
0            
01x2x6+1dx\int\limits_{0}^{1} \frac{x^{2}}{x^{6} + 1}\, dx
Integral(x^2/(1 + x^6), (x, 0, 1))
Detail solution
  1. Let u=x3u = x^{3}.

    Then let du=3x2dxdu = 3 x^{2} dx and substitute dudu:

    13u2+3du\int \frac{1}{3 u^{2} + 3}\, du

    1. The integral of 1u2+1\frac{1}{u^{2} + 1} is atan(u)3\frac{\operatorname{atan}{\left(u \right)}}{3}.

    Now substitute uu back in:

    atan(x3)3\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}

  2. Add the constant of integration:

    atan(x3)3+constant\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}+ \mathrm{constant}


The answer is:

atan(x3)3+constant\frac{\operatorname{atan}{\left(x^{3} \right)}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                        
 |                         
 |    2                / 3\
 |   x             atan\x /
 | ------ dx = C + --------
 |      6             3    
 | 1 + x                   
 |                         
/                          
arctanx33{{\arctan x^3}\over{3}}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
The answer [src]
pi
--
12
π12{{\pi}\over{12}}
=
=
pi
--
12
π12\frac{\pi}{12}
Numerical answer [src]
0.261799387799149
0.261799387799149
The graph
Integral of (x^2)/(1+x^6) dx

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