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x*e^[ln(8x)-(4x^2)]
Solving integrals/ x*e^[ln(8x)-(4x^2)]

Integral of x*e^[ln(8x)-(4x^2)] 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   
 |     log(8*x) - 4*x    
 |  x*E                dx
 |                       
/                        
0
$$\int\limits_{0}^{1} e^{- 4 x^{2} + \log{\left(8 x \right)}} x\, dx$$ 
Integral(x*E^(log(8*x) - 4*x^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                      
 |                                                       
 |                  2                 2     ____         
 |    log(8*x) - 4*x              -4*x    \/ pi *erf(2*x)
 | x*E                dx = C - x*e      + ---------------
 |                                               4       
/
$$\int e^{- 4 x^{2} + \log{\left(8 x \right)}} x\, dx = C - x e^{- 4 x^{2}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(2 x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          ____       
   -4   \/ pi *erf(2)
- e   + -------------
              4
$$- \frac{1}{e^{4}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(2 \right)}}{4}$$ 
=
= 
          ____       
   -4   \/ pi *erf(2)
- e   + -------------
              4
$$- \frac{1}{e^{4}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(2 \right)}}{4}$$ 
-exp(-4) + sqrt(pi)*erf(2)/4
Numerical answer [src] 
0.422725056492477
0.422725056492477
The graph
Integral of x*e^[ln(8x)-(4x^2)] dx

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

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