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1/(x^6+x^4)
Solving integrals/ 1/(x^6+x^4)

Integral of 1/(x^6+x^4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |   6    4   
 |  x  + x    
 |            
/             
0
$$\int\limits_{0}^{1} \frac{1}{x^{6} + x^{4}}\, dx$$ 
Integral(1/(x^6 + x^4), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Integrate term-by-term:

      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)

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

      1. The integral of is when :

      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    1            
 | ------- dx = C + - - ---- + atan(x)
 |  6    4          x      3          
 | x  + x               3*x           
 |                                    
/
$$\int \frac{1}{x^{6} + x^{4}}\, dx = C + \operatorname{atan}{\left(x \right)} + \frac{1}{x} - \frac{1}{3 x^{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo
$$\infty$$ 
=
= 
oo
$$\infty$$ 
oo
Numerical answer [src] 
7.81431122445857e+56
7.81431122445857e+56
The graph
Integral of 1/(x^6+x^4) dx

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

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