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Solving integrals/ e^(3cosx)*sinxdx

Integral of e^(3cosx)*sinxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |   3*cos(x)          
 |  E        *sin(x) dx
 |                     
/                      
0
$$\int\limits_{0}^{1} e^{3 \cos{\left(x \right)}} \sin{\left(x \right)}\, dx$$ 
Integral(E^(3*cos(x))*sin(x), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                            3*cos(x)
 |  3*cos(x)                 e        
 | E        *sin(x) dx = C - ---------
 |                               3    
/
$$\int e^{3 \cos{\left(x \right)}} \sin{\left(x \right)}\, dx = C - \frac{e^{3 \cos{\left(x \right)}}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   3*cos(1)    3
  e           e 
- --------- + --
      3       3
$$- \frac{e^{3 \cos{\left(1 \right)}}}{3} + \frac{e^{3}}{3}$$ 
=
= 
   3*cos(1)    3
  e           e 
- --------- + --
      3       3
$$- \frac{e^{3 \cos{\left(1 \right)}}}{3} + \frac{e^{3}}{3}$$ 
-exp(3*cos(1))/3 + exp(3)/3
Numerical answer [src] 
5.0092872637828
5.0092872637828

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

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