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Solving integrals/ sqrt(x)*exp^(-x)

Integral of sqrt(x)*exp^(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo             
  /             
 |              
 |    ___  -x   
 |  \/ x *E   dx
 |              
/               
0
∫0∞e−xx dx\int\limits_{0}^{\infty} e^{- x} \sqrt{x}\, dx 
Integral(sqrt(x)*E^(-x), (x, 0, oo))
Detail solution

    UpperGammaRule(a=-1, e=1/2, context=E**(-x)*sqrt(x), symbol=x)

  1. Add the constant of integration:

    −xe−x−πerfc⁡(x)2+constant- \sqrt{x} e^{- x} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}}{2}+ \mathrm{constant}

The answer is:

−xe−x−πerfc⁡(x)2+constant- \sqrt{x} e^{- x} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                 
 |                                  ____     /  ___\
 |   ___  -x            ___  -x   \/ pi *erfc\\/ x /
 | \/ x *E   dx = C - \/ x *e   - ------------------
 |                                        2         
/
∫e−xx dx=C−xe−x−πerfc⁡(x)2\int e^{- x} \sqrt{x}\, dx = C - \sqrt{x} e^{- x} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}}{2}
Simplify
The answer [src] 
  ____
\/ pi 
------
  2
π2\frac{\sqrt{\pi}}{2} 
=
= 
  ____
\/ pi 
------
  2
π2\frac{\sqrt{\pi}}{2} 
sqrt(pi)/2

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

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