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sin(log(x))/

Integral of sin(log(x))/ dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
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 |  sin(log(x)) dx
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$$\int\limits_{0}^{1} \sin{\left(\log{\left(x \right)} \right)}\, dx$$
Integral(sin(log(x)), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. Use integration by parts, noting that the integrand eventually repeats itself.

      1. For the integrand :

        Let and let .

        Then .

      2. For the integrand :

        Let and let .

        Then .

      3. Notice that the integrand has repeated itself, so move it to one side:

        Therefore,

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                  
 |                      x*sin(log(x))   x*cos(log(x))
 | sin(log(x)) dx = C + ------------- - -------------
 |                            2               2      
/                                                    
$$\int \sin{\left(\log{\left(x \right)} \right)}\, dx = C + \frac{x \sin{\left(\log{\left(x \right)} \right)}}{2} - \frac{x \cos{\left(\log{\left(x \right)} \right)}}{2}$$
The graph
The answer [src]
-1/2
$$- \frac{1}{2}$$
=
=
-1/2
$$- \frac{1}{2}$$
-1/2
Numerical answer [src]
-0.5
-0.5
The graph
Integral of sin(log(x))/ dx

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