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

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

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1/2             
   /              
  |               
  |  1 + cos(x)   
  |  ---------- dx
  |       2       
  |      x        
  |               
 /                
3/10              
$$\int\limits_{\frac{3}{10}}^{\frac{1}{2}} \frac{\cos{\left(x \right)} + 1}{x^{2}}\, dx$$
Integral((1 + cos(x))/(x^2), (x, 3/10, 1/2))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. Don't know the steps in finding this integral.

      But the integral is

    1. The integral of is when :

    The result is:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                      
 |                                       
 | 1 + cos(x)          1           cos(x)
 | ---------- dx = C - - - Si(x) - ------
 |      2              x             x   
 |     x                                 
 |                                       
/                                        
$$-{{1}\over{x}}-{{i\,\Gamma\left(-1 , i\,x\right)-i\,\Gamma\left(-1 , -i\,x\right)}\over{2}}$$
The graph
The answer [src]
4                          10*cos(3/10)           
- - Si(1/2) - 2*cos(1/2) + ------------ + Si(3/10)
3                               3                 
$$-{{3\,i\,\Gamma\left(-1 , {{i}\over{2}}\right)-3\,i\,\Gamma\left(-1 , {{3\,i}\over{10}}\right)+3\,i\,\Gamma\left(-1 , -{{3\,i}\over{10 }}\right)-3\,i\,\Gamma\left(-1 , -{{i}\over{2}}\right)-8}\over{6}}$$
=
=
4                          10*cos(3/10)           
- - Si(1/2) - 2*cos(1/2) + ------------ + Si(3/10)
3                               3                 
$$- 2 \cos{\left(\frac{1}{2} \right)} - \operatorname{Si}{\left(\frac{1}{2} \right)} + \operatorname{Si}{\left(\frac{3}{10} \right)} + \frac{4}{3} + \frac{10 \cos{\left(\frac{3}{10} \right)}}{3}$$
Numerical answer [src]
2.56801979906858
2.56801979906858
The graph
Integral of (1+cos(x))/x^2 dx

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