Mister Exam

Other calculators

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

Integral of sqrt(x)*e^(-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∞xe−x dx\int\limits_{0}^{\infty} \sqrt{x} e^{- x}\, dx
Simplify
Detail solution

    UpperGammaRule(a=-1, e=1/2, context=sqrt(x)/E**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         
/
2 (π erf(x)4−x e−x2)2\,\left({{\sqrt{\pi}\,\mathrm{erf}\left(\sqrt{x}\right)}\over{4}}- {{\sqrt{x}\,e^ {- x }}\over{2}}\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9001
Plot the graph f(x)
The answer [src] 
  ____
\/ pi 
------
  2
π2\frac{\sqrt{\pi}}{2} 
=
= 
  ____
\/ pi 
------
  2
π2\frac{\sqrt{\pi}}{2}
Simplify
The graph
Integral of sqrt(x)*e^(-x) dx

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

    © Mister Exam – Calculator