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Solving integrals/ e^(-px)

Integral of e^(-px) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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

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

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