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e^(-2x)sinx
Solving integrals/ e^(-2x)sinx

Integral of e^(-2x)sinx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |   -2*x          
 |  E    *sin(x) dx
 |                 
/                  
0
∫01e−2xsin⁡(x) dx\int\limits_{0}^{1} e^{- 2 x} \sin{\left(x \right)}\, dx 
Integral(E^(-2*x)*sin(x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                          -2*x                  -2*x
 |  -2*x                 2*e    *sin(x)   cos(x)*e    
 | E    *sin(x) dx = C - -------------- - ------------
 |                             5               5      
/
∫e−2xsin⁡(x) dx=C−2e−2xsin⁡(x)5−e−2xcos⁡(x)5\int e^{- 2 x} \sin{\left(x \right)}\, dx = C - \frac{2 e^{- 2 x} \sin{\left(x \right)}}{5} - \frac{e^{- 2 x} \cos{\left(x \right)}}{5}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
Plot the graph f(x)
The answer [src] 
       -2                  -2
1   2*e  *sin(1)   cos(1)*e  
- - ------------ - ----------
5        5             5
−2sin⁡(1)5e2−cos⁡(1)5e2+15- \frac{2 \sin{\left(1 \right)}}{5 e^{2}} - \frac{\cos{\left(1 \right)}}{5 e^{2}} + \frac{1}{5} 
=
= 
       -2                  -2
1   2*e  *sin(1)   cos(1)*e  
- - ------------ - ----------
5        5             5
−2sin⁡(1)5e2−cos⁡(1)5e2+15- \frac{2 \sin{\left(1 \right)}}{5 e^{2}} - \frac{\cos{\left(1 \right)}}{5 e^{2}} + \frac{1}{5} 
1/5 - 2*exp(-2)*sin(1)/5 - cos(1)*exp(-2)/5
Numerical answer [src] 
0.139823321254641
0.139823321254641
The graph
Integral of e^(-2x)sinx dx

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

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