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Integral of sin(ln*x)/x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  pi              
  --              
  2               
 e                
  /               
 |                
 |  sin(log(x))   
 |  ----------- dx
 |       x        
 |                
/                 
1                 
$$\int\limits_{1}^{e^{\frac{\pi}{2}}} \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}\, dx$$
Integral(sin(log(x))/x, (x, 1, exp(pi/2)))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of sine is negative cosine:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Let .

          Then let and substitute :

          1. The integral of a constant times a function is the constant times the integral of the function:

            1. The integral of sine is negative cosine:

            So, the result is:

          Now substitute back in:

        So, the result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                                 
 | sin(log(x))                     
 | ----------- dx = C - cos(log(x))
 |      x                          
 |                                 
/                                  
$$\int \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}\, dx = C - \cos{\left(\log{\left(x \right)} \right)}$$
The graph
The answer [src]
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$$1$$
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$$1$$
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.