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cos(x)*e^(sin(x))
Solving integrals/ cos(x)*e^(sin(x))

Integral of cos(x)*e^(sin(x)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                  
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 |          sin(x)   
 |  cos(x)*E       dx
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/                    
0
∫01esin⁡(x)cos⁡(x) dx\int\limits_{0}^{1} e^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx 
Integral(cos(x)*E^sin(x), (x, 0, 1))
Detail solution

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

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

    ∫eu du\int e^{u}\, du

    1. The integral of the exponential function is itself.

      ∫eu du=eu\int e^{u}\, du = e^{u}

    Now substitute uu back in:

    esin⁡(x)e^{\sin{\left(x \right)}}

  2. 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)
 | cos(x)*E       dx = C + e      
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∫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
0.001.000.100.200.300.400.500.600.700.800.9003
Plot the graph f(x)
The answer [src] 
      sin(1)
-1 + e
−1+esin⁡(1)-1 + e^{\sin{\left(1 \right)}} 
=
= 
      sin(1)
-1 + e
−1+esin⁡(1)-1 + e^{\sin{\left(1 \right)}} 
-1 + exp(sin(1))
Numerical answer [src] 
1.31977682471585
1.31977682471585
The graph
Integral of cos(x)*e^(sin(x)) dx

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

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