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Integral of sinx/(sin2xcosx) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                   
  /                   
 |                    
 |       sin(x)       
 |  --------------- dx
 |  sin(2*x)*cos(x)   
 |                    
/                     
0                     
01sin(x)sin(2x)cos(x)dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(2 x \right)} \cos{\left(x \right)}}\, dx
Integral(sin(x)/((sin(2*x)*cos(x))), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

    sin(x)sin(2x)cos(x)=12cos2(x)\frac{\sin{\left(x \right)}}{\sin{\left(2 x \right)} \cos{\left(x \right)}} = \frac{1}{2 \cos^{2}{\left(x \right)}}

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

    12cos2(x)dx=1cos2(x)dx2\int \frac{1}{2 \cos^{2}{\left(x \right)}}\, dx = \frac{\int \frac{1}{\cos^{2}{\left(x \right)}}\, dx}{2}

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

      But the integral is

      sin(x)cos(x)\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}

    So, the result is: sin(x)2cos(x)\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)}}

  3. Now simplify:

    tan(x)2\frac{\tan{\left(x \right)}}{2}

  4. Add the constant of integration:

    tan(x)2+constant\frac{\tan{\left(x \right)}}{2}+ \mathrm{constant}


The answer is:

tan(x)2+constant\frac{\tan{\left(x \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                 
 |                                  
 |      sin(x)               sin(x) 
 | --------------- dx = C + --------
 | sin(2*x)*cos(x)          2*cos(x)
 |                                  
/                                   
sin(x)sin(2x)cos(x)dx=C+sin(x)2cos(x)\int \frac{\sin{\left(x \right)}}{\sin{\left(2 x \right)} \cos{\left(x \right)}}\, dx = C + \frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)}}
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
The answer [src]
 sin(1) 
--------
2*cos(1)
sin(1)2cos(1)\frac{\sin{\left(1 \right)}}{2 \cos{\left(1 \right)}}
=
=
 sin(1) 
--------
2*cos(1)
sin(1)2cos(1)\frac{\sin{\left(1 \right)}}{2 \cos{\left(1 \right)}}
sin(1)/(2*cos(1))
Numerical answer [src]
0.778703862327451
0.778703862327451

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