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Solving integrals/ e^(-2ax)*

Integral of e^(-2ax)* dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |   -2*a*x   
 |  E       dx
 |            
/             
0
$$\int\limits_{0}^{1} e^{- 2 a x}\, dx$$ 
Integral(E^((-2*a)*x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                 //  -2*a*x             \
 |                  ||-e                   |
 |  -2*a*x          ||---------  for a != 0|
 | E       dx = C + |<   2*a               |
 |                  ||                     |
/                   ||    x      otherwise |
                    \\                     /
$$\int e^{- 2 a x}\, dx = C + \begin{cases} - \frac{e^{- 2 a x}}{2 a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/       -2*a                                  
| 1    e                                      
|--- - -----  for And(a > -oo, a < oo, a != 0)
<2*a    2*a                                   
|                                             
|     1                  otherwise            
\
$$\begin{cases} \frac{1}{2 a} - \frac{e^{- 2 a}}{2 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\1 & \text{otherwise} \end{cases}$$ 
=
= 
/       -2*a                                  
| 1    e                                      
|--- - -----  for And(a > -oo, a < oo, a != 0)
<2*a    2*a                                   
|                                             
|     1                  otherwise            
\
$$\begin{cases} \frac{1}{2 a} - \frac{e^{- 2 a}}{2 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\1 & \text{otherwise} \end{cases}$$ 
Piecewise((1/(2*a) - exp(-2*a)/(2*a), (a > -oo)∧(a < oo)∧(Ne(a, 0))), (1, True))

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

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