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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)
$$\int 2^{x} x\, dx = \frac{2^{x} \left(x \log{\left(2 \right)} - 1\right)}{\log{\left(2 \right)}^{2}} + C$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   1      2*(-1 + log(2))
------- + ---------------
   2             2       
log (2)       log (2)
$$\frac{2 \left(-1 + \log{\left(2 \right)}\right)}{\log{\left(2 \right)}^{2}} + \frac{1}{\log{\left(2 \right)}^{2}}$$ 
=
= 
   1      2*(-1 + log(2))
------- + ---------------
   2             2       
log (2)       log (2)
$$\frac{2 \left(-1 + \log{\left(2 \right)}\right)}{\log{\left(2 \right)}^{2}} + \frac{1}{\log{\left(2 \right)}^{2}}$$ 
log(2)^(-2) + 2*(-1 + log(2))/log(2)^2
Numerical answer [src] 
0.804021100772319
0.804021100772319
The graph
Integral of x*2^x dx

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

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