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sin(3*x)/sin(2*x)
Solving integrals/ sin(3*x)/sin(2*x)

Integral of sin(3*x)/sin(2*x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  sin(3*x)   
 |  -------- dx
 |  sin(2*x)   
 |             
/              
0
$$\int\limits_{0}^{1} \frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\, dx$$ 
Integral(sin(3*x)/sin(2*x), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Integrate term-by-term:

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

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

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

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    The result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                               
 |                                                                
 | sin(3*x)                     log(1 + sin(x))   log(-1 + sin(x))
 | -------- dx = C + 2*sin(x) - --------------- + ----------------
 | sin(2*x)                            4                 4        
 |                                                                
/
$$\int \frac{\sin{\left(3 x \right)}}{\sin{\left(2 x \right)}}\, dx = C + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + 2 \sin{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
           log(1 + sin(1))   log(1 - sin(1))
2*sin(1) - --------------- + ---------------
                  4                 4
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} + 2 \sin{\left(1 \right)}$$ 
=
= 
           log(1 + sin(1))   log(1 - sin(1))
2*sin(1) - --------------- + ---------------
                  4                 4
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} + 2 \sin{\left(1 \right)}$$ 
2*sin(1) - log(1 + sin(1))/4 + log(1 - sin(1))/4
Numerical answer [src] 
1.06984638417403
1.06984638417403
The graph
Integral of sin(3*x)/sin(2*x) dx

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

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