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Integral of (sin(lnx)/x)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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 |  sin(log(x))*-*1 dx
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$$\int\limits_{0}^{1} \sin{\left(\log{\left(x \right)} \right)} \frac{1}{x} 1\, dx$$
Integral(sin(log(x))*1/x, (x, 0, 1))
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]
  /                                    
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 |             1                       
 | sin(log(x))*-*1 dx = C - cos(log(x))
 |             x                       
 |                                     
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$$\int \sin{\left(\log{\left(x \right)} \right)} \frac{1}{x} 1\, dx = C - \cos{\left(\log{\left(x \right)} \right)}$$
The answer [src]
<-2, 0>
$$\left\langle -2, 0\right\rangle$$
=
=
<-2, 0>
$$\left\langle -2, 0\right\rangle$$
Numerical answer [src]
0.0141500631560091
0.0141500631560091

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