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Integral of 1/xsin(1/x) dx

The solution

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 oo          
  /          
 |           
 |     /1\   
 |  sin|-|   
 |     \x/   
 |  ------ dx
 |    x      
 |           
/            
1

$$\int\limits_{1}^{\infty} \frac{\sin{\left(\frac{1}{x} \right)}}{x}\, dx$$

Integral(sin(1/x)/x, (x, 1, oo))

Detail solution

Let $u = \frac{1}{x}$ .

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                     
 |                      
 |    /1\               
 | sin|-|               
 |    \x/            /1\
 | ------ dx = C - Si|-|
 |   x               \x/
 |                      
/

$$\int \frac{\sin{\left(\frac{1}{x} \right)}}{x}\, dx = C - \operatorname{Si}{\left(\frac{1}{x} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

Si(1)

$$\operatorname{Si}{\left(1 \right)}$$

Si(1)

$$\operatorname{Si}{\left(1 \right)}$$

Si(1)

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

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Identical expressions

Integral of 1/xsin(1/x) dx

Limits of integration:

The graph:

Piecewise:

The solution