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e^sinx×cosx
Solving integrals/ e^sinx×cosx

Integral of e^sinx×cosx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 pi                  
  /                  
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 |   sin(x)          
 |  e      *cos(x) dx
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/                    
pi                   
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2
∫π2πesin⁡(x)cos⁡(x) dx\int\limits_{\frac{\pi}{2}}^{\pi} e^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx 
Integral(E^sin(x)*cos(x), (x, pi/2, pi))
Detail solution

  1. Let u=esin⁡(x)u = e^{\sin{\left(x \right)}}.

    Then let du=esin⁡(x)cos⁡(x)dxdu = e^{\sin{\left(x \right)}} \cos{\left(x \right)} dx and substitute dudu:

    ∫1 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

    Now substitute uu back in:

    esin⁡(x)e^{\sin{\left(x \right)}}

  2. Now simplify:

    esin⁡(x)e^{\sin{\left(x \right)}}

  3. Add the constant of integration:

    esin⁡(x)+constante^{\sin{\left(x \right)}}+ \mathrm{constant}

The answer is:

esin⁡(x)+constante^{\sin{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                                
 |  sin(x)                  sin(x)
 | e      *cos(x) dx = C + e      
 |                                
/
∫esin⁡(x)cos⁡(x) dx=C+esin⁡(x)\int e^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx = C + e^{\sin{\left(x \right)}}
Simplify
The graph
1.61.71.81.92.02.12.22.32.42.52.62.72.82.93.03.15-5
Plot the graph f(x)
The answer [src] 
1 - e
1−e1 - e 
=
= 
1 - e
1−e1 - e
Упростить
Numerical answer [src] 
-1.71828182845905
-1.71828182845905
The graph
Integral of e^sinx×cosx dx

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

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