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sinx/(2cosx)/2

Integral of sinx/(2cosx)/2 dx

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The solution

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  1              
  /              
 |               
 |    sin(x)     
 |  ---------- dx
 |  2*cos(x)*2   
 |               
/                
0                
01sin(x)22cos(x)dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{2 \cdot 2 \cos{\left(x \right)}}\, dx
Integral(sin(x)/((2*cos(x))*2), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    sin(x)22cos(x)dx=sin(x)2cos(x)dx2\int \frac{\sin{\left(x \right)}}{2 \cdot 2 \cos{\left(x \right)}}\, dx = \frac{\int \frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)}}\, dx}{2}

    1. Let u=2cos(x)u = 2 \cos{\left(x \right)}.

      Then let du=2sin(x)dxdu = - 2 \sin{\left(x \right)} dx and substitute du2- \frac{du}{2}:

      14udu\int \frac{1}{4 u}\, du

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

        (12u)du=1udu2\int \left(- \frac{1}{2 u}\right)\, du = - \frac{\int \frac{1}{u}\, du}{2}

        1. The integral of 1u\frac{1}{u} is log(u)\log{\left(u \right)}.

        So, the result is: log(u)2- \frac{\log{\left(u \right)}}{2}

      Now substitute uu back in:

      log(2cos(x))2- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{2}

    So, the result is: log(2cos(x))4- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{4}

  2. Add the constant of integration:

    log(2cos(x))4+constant- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{4}+ \mathrm{constant}


The answer is:

log(2cos(x))4+constant- \frac{\log{\left(2 \cos{\left(x \right)} \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                                 
 |                                  
 |   sin(x)            log(2*cos(x))
 | ---------- dx = C - -------------
 | 2*cos(x)*2                4      
 |                                  
/                                   
logcosx4-{{\log \cos x}\over{4}}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.5
The answer [src]
-log(cos(1)) 
-------------
      4      
logcos14-{{\log \cos 1}\over{4}}
=
=
-log(cos(1)) 
-------------
      4      
log(cos(1))4- \frac{\log{\left(\cos{\left(1 \right)} \right)}}{4}
Numerical answer [src]
0.153906617596504
0.153906617596504
The graph
Integral of sinx/(2cosx)/2 dx

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