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Solving integrals/ -(e^x)*sin(y)

Integral of -(e^x)*sin(y) dx

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The solution

You have entered [src] 
  x              
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 |    x          
 |  -E *sin(y) dx
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∫0x−exsin⁡(y) dx\int\limits_{0}^{x} - e^{x} \sin{\left(y \right)}\, dx 
Integral((-E^x)*sin(y), (x, 0, x))
Detail solution

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

    ∫−exsin⁡(y) dx=sin⁡(y)∫(−ex) dx\int - e^{x} \sin{\left(y \right)}\, dx = \sin{\left(y \right)} \int \left(- e^{x}\right)\, dx

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

      ∫(−ex) dx=−∫ex dx\int \left(- e^{x}\right)\, dx = - \int e^{x}\, dx

      1. The integral of the exponential function is itself.

        ∫ex dx=ex\int e^{x}\, dx = e^{x}

      So, the result is: −ex- e^{x}

    So, the result is: −exsin⁡(y)- e^{x} \sin{\left(y \right)}

  2. Add the constant of integration:

    −exsin⁡(y)+constant- e^{x} \sin{\left(y \right)}+ \mathrm{constant}

The answer is:

−exsin⁡(y)+constant- e^{x} \sin{\left(y \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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 |   x                  x       
 | -E *sin(y) dx = C - e *sin(y)
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∫−exsin⁡(y) dx=C−exsin⁡(y)\int - e^{x} \sin{\left(y \right)}\, dx = C - e^{x} \sin{\left(y \right)}
Simplify
The answer [src] 
   x                
- e *sin(y) + sin(y)
−exsin⁡(y)+sin⁡(y)- e^{x} \sin{\left(y \right)} + \sin{\left(y \right)} 
=
= 
   x                
- e *sin(y) + sin(y)
−exsin⁡(y)+sin⁡(y)- e^{x} \sin{\left(y \right)} + \sin{\left(y \right)} 
-exp(x)*sin(y) + sin(y)

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

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