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Solving integrals/ x*exp(-ax)*dx

Integral of x*exp(-ax)*dx dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
 10           
  /           
 |            
 |     -a*x   
 |  x*e     dx
 |            
/             
0
$$\int\limits_{0}^{10} x e^{- a x}\, dx$$ 
Integral(x*exp((-a)*x), (x, 0, 10))
The answer (Indefinite) [src] 
                    //         2                    \                          
                    ||        x                     |                          
                    ||        --           for a = 0|                          
                    ||        2                     |                          
  /                 ||                              |     //   x     for a = 0\
 |                  ||/ -a*x                        |     ||                  |
 |    -a*x          |||e           2                |     ||  -a*x            |
 | x*e     dx = C - |<|-----  for a  != 0           | + x*|<-e                |
 |                  |||   2                         |     ||-------  otherwise|
/                   ||<  a                 otherwise|     ||   a              |
                    |||                             |     \\                  /
                    ||| -x                          |                          
                    ||| ---    otherwise            |                          
                    ||\  a                          |                          
                    \\                              /
$$\int x e^{- a x}\, dx = C + x \left(\begin{cases} x & \text{for}\: a = 0 \\- \frac{e^{- a x}}{a} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: a = 0 \\\begin{cases} \frac{e^{- a x}}{a^{2}} & \text{for}\: a^{2} \neq 0 \\- \frac{x}{a} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/                  -10*a                                  
|1    (-1 - 10*a)*e                                       
|-- + ------------------  for And(a > -oo, a < oo, a != 0)
< 2            2                                          
|a            a                                           
|                                                         
\          50                        otherwise
$$\begin{cases} \frac{\left(- 10 a - 1\right) e^{- 10 a}}{a^{2}} + \frac{1}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\50 & \text{otherwise} \end{cases}$$ 
=
= 
/                  -10*a                                  
|1    (-1 - 10*a)*e                                       
|-- + ------------------  for And(a > -oo, a < oo, a != 0)
< 2            2                                          
|a            a                                           
|                                                         
\          50                        otherwise
$$\begin{cases} \frac{\left(- 10 a - 1\right) e^{- 10 a}}{a^{2}} + \frac{1}{a^{2}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\50 & \text{otherwise} \end{cases}$$ 
Piecewise((a^(-2) + (-1 - 10*a)*exp(-10*a)/a^2, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (50, True))

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

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