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x*2^(-x)
Solving integrals/ x*2^(-x)

Integral of x*2^(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |     -x   
 |  x*2   dx
 |          
/           
0
$$\int\limits_{0}^{1} 2^{- x} x\, dx$$ 
Integral(x*2^(-x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                  
 |                 -x                
 |    -x          2  *(-1 - x*log(2))
 | x*2   dx = C + -------------------
 |                         2         
/                       log (2)
$$\int 2^{- x} x\, dx = C + \frac{2^{- x} \left(- x \log{\left(2 \right)} - 1\right)}{\log{\left(2 \right)}^{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   1      -1 - log(2)
------- + -----------
   2            2    
log (2)    2*log (2)
$$\frac{-1 - \log{\left(2 \right)}}{2 \log{\left(2 \right)}^{2}} + \frac{1}{\log{\left(2 \right)}^{2}}$$ 
=
= 
   1      -1 - log(2)
------- + -----------
   2            2    
log (2)    2*log (2)
$$\frac{-1 - \log{\left(2 \right)}}{2 \log{\left(2 \right)}^{2}} + \frac{1}{\log{\left(2 \right)}^{2}}$$ 
log(2)^(-2) + (-1 - log(2))/(2*log(2)^2)
Numerical answer [src] 
0.319336970058322
0.319336970058322
The graph
Integral of x*2^(-x) dx

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

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