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Identical expressions
(sin1/x)/x^ two
( sinus of 1 divide by x) divide by x squared
( sinus of 1 divide by x) divide by x to the power of two
(sin1/x)/x2
sin1/x/x2
(sin1/x)/x²
(sin1/x)/x to the power of 2
sin1/x/x^2
(sin1 divide by x) divide by x^2
(sin1/x)/x^2dx

Integral of (sin1/x)/x^2 dx

The solution

You have entered [src]

 100           
 ---           
 157           
  /            
 |             
 |  /sin(1)\   
 |  |------|   
 |  \  x   /   
 |  -------- dx
 |      2      
 |     x       
 |             
/              
 50            
---            
157

$$\int\limits_{\frac{50}{157}}^{\frac{100}{157}} \frac{\frac{1}{x} \sin{\left(1 \right)}}{x^{2}}\, dx$$

Integral((sin(1)/x)/x^2, (x, 50/157, 100/157))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = \frac{1}{x}$ .
  
  Then let $du = - \frac{dx}{x^{2}}$ and substitute $- du \sin{\left(1 \right)}$ :
  
  $\int \left(- u \sin{\left(1 \right)}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = - \sin{\left(1 \right)} \int u\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $- \frac{u^{2} \sin{\left(1 \right)}}{2}$
  Now substitute $u$ back in:
  
  $- \frac{\sin{\left(1 \right)}}{2 x^{2}}$
Method #2
1. Let $u = \frac{1}{x^{2}}$ .
  
  Then let $du = - \frac{2 dx}{x^{3}}$ and substitute $- \frac{du \sin{\left(1 \right)}}{2}$ :
  
  $\int \left(- \frac{\sin{\left(1 \right)}}{2}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 1\, du = - \frac{\sin{\left(1 \right)} \int 1\, du}{2}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $- \frac{u \sin{\left(1 \right)}}{2}$
  Now substitute $u$ back in:
  
  $- \frac{\sin{\left(1 \right)}}{2 x^{2}}$
Method #3
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du \sin{\left(1 \right)}}{2}$ :
  
  $\int \frac{\sin{\left(1 \right)}}{2 u^{2}}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u^{2}}\, du = \frac{\sin{\left(1 \right)} \int \frac{1}{u^{2}}\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{u^{2}}\, du = - \frac{1}{u}$
    So, the result is: $- \frac{\sin{\left(1 \right)}}{2 u}$
  Now substitute $u$ back in:
  
  $- \frac{\sin{\left(1 \right)}}{2 x^{2}}$
Add the constant of integration:

$- \frac{\sin{\left(1 \right)}}{2 x^{2}}+ \mathrm{constant}$

The answer is:

$- \frac{\sin{\left(1 \right)}}{2 x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 | /sin(1)\                
 | |------|                
 | \  x   /          sin(1)
 | -------- dx = C - ------
 |     2                 2 
 |    x               2*x  
 |                         
/

$$\int \frac{\frac{1}{x} \sin{\left(1 \right)}}{x^{2}}\, dx = C - \frac{\sin{\left(1 \right)}}{2 x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

73947*sin(1)
------------
   20000

$$\frac{73947 \sin{\left(1 \right)}}{20000}$$

73947*sin(1)
------------
   20000

$$\frac{73947 \sin{\left(1 \right)}}{20000}$$

73947*sin(1)/20000

Numerical answer [src]

3.11121274567948

3.11121274567948

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

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How to use it?

Identical expressions

Integral of (sin1/x)/x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Method #3