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sin(2/x)/x^2dx

Solving integrals/ sin(2/x)/x^2

Integral of sin(2/x)/x^2 dx

The solution

You have entered [src]

 2           
 --          
 pi          
  /          
 |           
 |     /2\   
 |  sin|-|   
 |     \x/   
 |  ------ dx
 |     2     
 |    x      
 |           
/            
0

$$\int\limits_{0}^{\frac{2}{\pi}} \frac{\sin{\left(\frac{2}{x} \right)}}{x^{2}}\, dx$$

Integral(sin(2/x)/x^2, (x, 0, 2/pi))

Detail solution

Let $u = \frac{2}{x}$ .

Then let $du = - \frac{2 dx}{x^{2}}$ and substitute $- \frac{du}{2}$ :

$\int \left(- \frac{\sin{\left(u \right)}}{2}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = - \frac{\int \sin{\left(u \right)}\, du}{2}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $\frac{\cos{\left(u \right)}}{2}$
Now substitute $u$ back in:

$\frac{\cos{\left(\frac{2}{x} \right)}}{2}$
Add the constant of integration:

$\frac{\cos{\left(\frac{2}{x} \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\cos{\left(\frac{2}{x} \right)}}{2}+ \mathrm{constant}$

The graph

Plot the graph f(x)

The answer [src]

<-1, 0>

$$\left\langle -1, 0\right\rangle$$

<-1, 0>

$$\left\langle -1, 0\right\rangle$$

AccumBounds(-1, 0)

Numerical answer [src]

-6.28438770997311e+18

-6.28438770997311e+18

The graph

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

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Identical expressions

Integral of sin(2/x)/x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution