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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] 
 1/7           
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 |    ___  x   
 |  \/ x *e  dx
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0
∫017xex dx\int\limits_{0}^{\frac{1}{7}} \sqrt{x} e^{x}\, dx 
Integral(sqrt(x)*exp(x), (x, 0, 1/7))
Detail solution

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

  1. Now simplify:

    xex+πxerfc⁡(−x)2−x\sqrt{x} e^{x} + \frac{\sqrt{\pi} \sqrt{x} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2 \sqrt{- x}}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
                           /              ____     /  ____\\
  /                    ___ |  ____  x   \/ pi *erfc\\/ -x /|
 |                   \/ x *|\/ -x *e  + -------------------|
 |   ___  x                \                     2         /
 | \/ x *e  dx = C + ---------------------------------------
 |                                      ____                
/                                     \/ -x
∫xex dx=C+x(−xex+πerfc⁡(−x)2)−x\int \sqrt{x} e^{x}\, dx = C + \frac{\sqrt{x} \left(\sqrt{- x} e^{x} + \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{- x} \right)}}{2}\right)}{\sqrt{- x}}
Simplify
The graph
0.000.010.020.030.040.050.060.070.080.090.100.110.120.130.140.00.5
Plot the graph f(x)
The answer [src] 
                         /    ___\
                 ____    |I*\/ 7 |
  ___  1/7   I*\/ pi *erf|-------|
\/ 7 *e                  \   7   /
---------- + ---------------------
    7                  2
iπerf⁡(7i7)2+7e177\frac{i \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{7} i}{7} \right)}}{2} + \frac{\sqrt{7} e^{\frac{1}{7}}}{7} 
=
= 
                         /    ___\
                 ____    |I*\/ 7 |
  ___  1/7   I*\/ pi *erf|-------|
\/ 7 *e                  \   7   /
---------- + ---------------------
    7                  2
iπerf⁡(7i7)2+7e177\frac{i \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{7} i}{7} \right)}}{2} + \frac{\sqrt{7} e^{\frac{1}{7}}}{7} 
sqrt(7)*exp(1/7)/7 + i*sqrt(pi)*erf(i*sqrt(7)/7)/2
Numerical answer [src] 
0.0392454652807396
0.0392454652807396

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

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