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1/(x^4+x^2)
Solving integrals/ 1/(x^4+x^2)

Integral of 1/(x^4+x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |   4    2   
 |  x  + x    
 |            
/             
0
$$\int\limits_{0}^{1} \frac{1}{x^{4} + x^{2}}\, dx$$ 
Integral(1/(x^4 + x^2), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

        PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=1, c=1, context=1/(x**2 + 1), symbol=x), True), (ArccothRule(a=1, b=1, c=1, context=1/(x**2 + 1), symbol=x), False), (ArctanhRule(a=1, b=1, c=1, context=1/(x**2 + 1), symbol=x), False)], context=1/(x**2 + 1), symbol=x)

      So, the result is:

    1. The integral of is when :

    The result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            
 |                             
 |    1             1          
 | ------- dx = C - - - atan(x)
 |  4    2          x          
 | x  + x                      
 |                             
/
$$\int \frac{1}{x^{4} + x^{2}}\, dx = C - \operatorname{atan}{\left(x \right)} - \frac{1}{x}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
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$$\infty$$ 
=
= 
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$$\infty$$ 
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Numerical answer [src] 
1.3793236779486e+19
1.3793236779486e+19
The graph
Integral of 1/(x^4+x^2) dx

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

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