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e^(2x)*sin(3x)
Solving integrals/ e^(2x)*sin(3x)

Integral of e^(2x)*sin(3x) dx

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The graph:

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The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |   2*x            
 |  E   *sin(3*x) dx
 |                  
/                   
0
∫01e2xsin⁡(3x) dx\int\limits_{0}^{1} e^{2 x} \sin{\left(3 x \right)}\, dx 
Integral(E^(2*x)*sin(3*x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                        
 |                                    2*x      2*x         
 |  2*x                   3*cos(3*x)*e      2*e   *sin(3*x)
 | E   *sin(3*x) dx = C - --------------- + ---------------
 |                               13                13      
/
∫e2xsin⁡(3x) dx=C+2e2xsin⁡(3x)13−3e2xcos⁡(3x)13\int e^{2 x} \sin{\left(3 x \right)}\, dx = C + \frac{2 e^{2 x} \sin{\left(3 x \right)}}{13} - \frac{3 e^{2 x} \cos{\left(3 x \right)}}{13}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
               2      2       
3    3*cos(3)*e    2*e *sin(3)
-- - ----------- + -----------
13        13            13
2e2sin⁡(3)13+313−3e2cos⁡(3)13\frac{2 e^{2} \sin{\left(3 \right)}}{13} + \frac{3}{13} - \frac{3 e^{2} \cos{\left(3 \right)}}{13} 
=
= 
               2      2       
3    3*cos(3)*e    2*e *sin(3)
-- - ----------- + -----------
13        13            13
2e2sin⁡(3)13+313−3e2cos⁡(3)13\frac{2 e^{2} \sin{\left(3 \right)}}{13} + \frac{3}{13} - \frac{3 e^{2} \cos{\left(3 \right)}}{13} 
3/13 - 3*cos(3)*exp(2)/13 + 2*exp(2)*sin(3)/13
Numerical answer [src] 
2.07929366132116
2.07929366132116
The graph
Integral of e^(2x)*sin(3x) dx

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

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