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Solving integrals/ sin(2(3-x))exp(x)

Integral of sin(2(3-x))exp(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3                     
  /                     
 |                      
 |                  x   
 |  sin(2*(3 - x))*e  dx
 |                      
/                       
0
$$\int\limits_{0}^{3} e^{x} \sin{\left(2 \left(3 - x\right) \right)}\, dx$$ 
Integral(sin(2*(3 - x))*exp(x), (x, 0, 3))
The answer (Indefinite) [src] 
  /                                                                
 |                             x                                  x
 |                 x          e *sin(-6 + 2*x)   2*cos(-6 + 2*x)*e 
 | sin(2*(3 - x))*e  dx = C - ---------------- + ------------------
 |                                   5                   5         
/
$$\int e^{x} \sin{\left(2 \left(3 - x\right) \right)}\, dx = C - \frac{e^{x} \sin{\left(2 x - 6 \right)}}{5} + \frac{2 e^{x} \cos{\left(2 x - 6 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                         3
  2*cos(6)   sin(6)   2*e 
- -------- - ------ + ----
     5         5       5
$$- \frac{2 \cos{\left(6 \right)}}{5} - \frac{\sin{\left(6 \right)}}{5} + \frac{2 e^{3}}{5}$$ 
=
= 
                         3
  2*cos(6)   sin(6)   2*e 
- -------- - ------ + ----
     5         5       5
$$- \frac{2 \cos{\left(6 \right)}}{5} - \frac{\sin{\left(6 \right)}}{5} + \frac{2 e^{3}}{5}$$ 
-2*cos(6)/5 - sin(6)/5 + 2*exp(3)/5
Numerical answer [src] 
7.70602975425471
7.70602975425471

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

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