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(1/(sqrt(2*pi)))*exp(-(x^2+1)/8)

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  • Integral of d{x}:
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  • Identical expressions

  • (one /(sqrt(two *pi)))*exp(-(x^ two + one)/ eight)
  • (1 divide by ( square root of (2 multiply by Pi ))) multiply by exponent of ( minus (x squared plus 1) divide by 8)
  • (one divide by ( square root of (two multiply by Pi ))) multiply by exponent of ( minus (x to the power of two plus one) divide by eight)
  • (1/(√(2*pi)))*exp(-(x^2+1)/8)
  • (1/(sqrt(2*pi)))*exp(-(x2+1)/8)
  • 1/sqrt2*pi*exp-x2+1/8
  • (1/(sqrt(2*pi)))*exp(-(x²+1)/8)
  • (1/(sqrt(2*pi)))*exp(-(x to the power of 2+1)/8)
  • (1/(sqrt(2pi)))exp(-(x^2+1)/8)
  • (1/(sqrt(2pi)))exp(-(x2+1)/8)
  • 1/sqrt2piexp-x2+1/8
  • 1/sqrt2piexp-x^2+1/8
  • (1 divide by (sqrt(2*pi)))*exp(-(x^2+1) divide by 8)
  • (1/(sqrt(2*pi)))*exp(-(x^2+1)/8)dx

  • Similar expressions

  • (1/(sqrt(2*pi)))*exp((x^2+1)/8)
  • (1/(sqrt(2*pi)))*exp(-(x^2-1)/8)
Solving integrals/ (1/(sqrt(2*pi)))*exp(-(x^2+1)/8)

Integral of (1/(sqrt(2*pi)))*exp(-(x^2+1)/8) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |                    2   
 |              -1 - x    
 |              -------   
 |       1         8      
 |  1*--------*e        dx
 |      ______            
 |    \/ 2*pi             
 |                        
/                         
84
$$\int\limits_{84}^{1} 1 \cdot \frac{1}{\sqrt{2 \pi}} e^{\frac{- x^{2} - 1}{8}}\, dx$$ 
Integral(1*exp(-x^2 - 1/8)/sqrt(2*pi), (x, 84, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

      ErfRule(a=-1/8, b=0, c=-1/8, context=exp(-x**2 - 1/8), symbol=x)

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                     
 |                                                                      
 |                   2                                                  
 |             -1 - x                                                   
 |             -------                          ___      /    ___\      
 |      1         8               ___   ____  \/ 2       |x*\/ 2 |  -1/8
 | 1*--------*e        dx = C + \/ 2 *\/ pi *--------*erf|-------|*e    
 |     ______                                    ____    \   4   /      
 |   \/ 2*pi                                 2*\/ pi                    
 |                                                                      
/
$${{e^ {- {{1}\over{8}} }\,\sqrt{\pi}\,\mathrm{erf}\left(x\right) }\over{2^{{{3}\over{2}}}\,\sqrt{\pi}}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   /  ___\                            
   |\/ 2 |  -1/8      /     ___\  -1/8
erf|-----|*e     - erf\21*\/ 2 /*e    
   \  4  /
$$-{{{{e^ {- {{1}\over{8}} }\,\sqrt{\pi}\,\mathrm{erf}\left(84\right) }\over{2}}-{{e^ {- {{1}\over{8}} }\,\sqrt{\pi}\,\mathrm{erf}\left(1 \right)}\over{2}}}\over{\sqrt{2}\,\sqrt{\pi}}}$$ 
=
= 
   /  ___\                            
   |\/ 2 |  -1/8      /     ___\  -1/8
erf|-----|*e     - erf\21*\/ 2 /*e    
   \  4  /
$$- \frac{\operatorname{erf}{\left(21 \sqrt{2} \right)}}{e^{\frac{1}{8}}} + \frac{\operatorname{erf}{\left(\frac{\sqrt{2}}{4} \right)}}{e^{\frac{1}{8}}}$$
Упростить
Numerical answer [src] 
-0.544566844513516
-0.544566844513516
The graph
Integral of (1/(sqrt(2*pi)))*exp(-(x^2+1)/8) dx

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

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