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Integral of (cos(lnx))*(dx/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                   
  /                   
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 |                1   
 |  cos(log(x))*1*- dx
 |                x   
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \cos{\left(\log{\left(x \right)} \right)} 1 \cdot \frac{1}{x}\, dx$$
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of cosine is sine:

      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 cosine is sine:

            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]
  /                                    
 |                                     
 |               1                     
 | cos(log(x))*1*- dx = C + sin(log(x))
 |               x                     
 |                                     
/                                      
$$\sin \log x$$
The answer [src]
<-1, 1>
$$\int_{0}^{1}{{{\cos \log x}\over{x}}\;dx}$$
=
=
<-1, 1>
$$\left\langle -1, 1\right\rangle$$
Numerical answer [src]
0.110056905018961
0.110056905018961

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