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Limit of the function:
(1+cos(x))/x^2
Identical expressions
(one +cos(x))/x^ two
(1 plus co sinus of e of (x)) divide by x squared
(one plus co sinus of e of (x)) divide by x to the power of two
(1+cos(x))/x2
1+cosx/x2
(1+cos(x))/x²
(1+cos(x))/x to the power of 2
1+cosx/x^2
(1+cos(x)) divide by x^2
(1+cos(x))/x^2dx
Similar expressions
(1-cos(x))/x^2
(1+cosx)/x^2

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

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

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

Rewrite the integrand:

$\frac{\cos{\left(x \right)} + 1}{x^{2}} = \frac{\cos{\left(x \right)}}{x^{2}} + \frac{1}{x^{2}}$
Integrate term-by-term:
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \operatorname{Si}{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
The result is: $- \operatorname{Si}{\left(x \right)} - \frac{\cos{\left(x \right)}}{x} - \frac{1}{x}$
Now simplify:

$- \frac{x \operatorname{Si}{\left(x \right)} + \cos{\left(x \right)} + 1}{x}$
Add the constant of integration:

$- \frac{x \operatorname{Si}{\left(x \right)} + \cos{\left(x \right)} + 1}{x}+ \mathrm{constant}$

The answer is:

$- \frac{x \operatorname{Si}{\left(x \right)} + \cos{\left(x \right)} + 1}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                      
 |                                       
 | 1 + cos(x)          1           cos(x)
 | ---------- dx = C - - - Si(x) - ------
 |      2              x             x   
 |     x                                 
 |                                       
/

$$-{{1}\over{x}}-{{i\,\Gamma\left(-1 , i\,x\right)-i\,\Gamma\left(-1 , -i\,x\right)}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

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

$$- 2 \cos{\left(\frac{1}{2} \right)} - \operatorname{Si}{\left(\frac{1}{2} \right)} + \operatorname{Si}{\left(\frac{3}{10} \right)} + \frac{4}{3} + \frac{10 \cos{\left(\frac{3}{10} \right)}}{3}$$

Simplify

Numerical answer [src]

2.56801979906858

2.56801979906858

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution