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sinx/cosx*cosx
Solving integrals/ sinx/cosx*cosx

Integral of sinx/cosx*cosx dx

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The solution

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  1                 
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 |  sin(x)*cos(x)   
 |  ------------- dx
 |      cos(x)      
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0
∫01sin⁡(x)cos⁡(x)cos⁡(x) dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)}}\, dx 
Integral(sin(x)*cos(x)/cos(x), (x, 0, 1))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

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

      Then let du=sin⁡(x)dxcos⁡2(x)du = \frac{\sin{\left(x \right)} dx}{\cos^{2}{\left(x \right)}} and substitute dudu:

      ∫1u2 du\int \frac{1}{u^{2}}\, du

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫1u2 du=−1u\int \frac{1}{u^{2}}\, du = - \frac{1}{u}

      Now substitute uu back in:

      −cos⁡(x)- \cos{\left(x \right)}

    Method #2

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

      Then let du=−sin⁡(x)dxdu = - \sin{\left(x \right)} dx and substitute −du- du:

      ∫1 du\int 1\, du

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

        ∫(−1) du=−∫1 du\int \left(-1\right)\, du = - \int 1\, du

        1. The integral of a constant is the constant times the variable of integration:

          ∫1 du=u\int 1\, du = u

        So, the result is: −u- u

      Now substitute uu back in:

      −cos⁡(x)- \cos{\left(x \right)}

  2. Add the constant of integration:

    −cos⁡(x)+constant- \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

−cos⁡(x)+constant- \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 | sin(x)*cos(x)                
 | ------------- dx = C - cos(x)
 |     cos(x)                   
 |                              
/
∫sin⁡(x)cos⁡(x)cos⁡(x) dx=C−cos⁡(x)\int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)}}\, dx = C - \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
1 - cos(1)
1−cos⁡(1)1 - \cos{\left(1 \right)} 
=
= 
1 - cos(1)
1−cos⁡(1)1 - \cos{\left(1 \right)}
Упростить
Numerical answer [src] 
0.45969769413186
0.45969769413186
The graph
Integral of sinx/cosx*cosx dx

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

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