Mister Exam

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Identical expressions
x^(- one / two)exp(-x)
x to the power of ( minus 1 divide by 2) exponent of ( minus x)
x to the power of ( minus one divide by two) exponent of ( minus x)
x(-1/2)exp(-x)
x-1/2exp-x
x^-1/2exp-x
x^(-1 divide by 2)exp(-x)
x^(-1/2)exp(-x)dx
Similar expressions
x^(1/2)exp(-x)
x^(-1/2)exp(x)

Integral of x^(-1/2)exp(-x) dx

The solution

You have entered [src]

 oo         
  /         
 |          
 |    -x    
 |   e      
 |  ----- dx
 |    ___   
 |  \/ x    
 |          
/           
0

$$\int\limits_{0}^{\infty} \frac{e^{- x}}{\sqrt{x}}\, dx$$

Integral(exp(-x)/sqrt(x), (x, 0, oo))

Detail solution

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

Add the constant of integration:

$- \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}+ \mathrm{constant}$

The answer is:

$- \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                  
 |   -x                             
 |  e               ____     /  ___\
 | ----- dx = C - \/ pi *erfc\\/ x /
 |   ___                            
 | \/ x                             
 |                                  
/

$$\int \frac{e^{- x}}{\sqrt{x}}\, dx = C - \sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ____
\/ pi

$$\sqrt{\pi}$$

  ____
\/ pi

$$\sqrt{\pi}$$

sqrt(pi)

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

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Identical expressions

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Integral of x^(-1/2)exp(-x) dx

Limits of integration:

The graph:

Piecewise:

The solution