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

The solution

You have entered [src]

  y               
  /               
 |                
 |       1        
 |  ----------- dx
 |   /       2\   
 |   \(x - 1) /   
 |  e             
 |                
/                 
-oo

$$\int\limits_{-\infty}^{y} \frac{1}{e^{\left(x - 1\right)^{2}}}\, dx$$

Integral(1/exp((x - 1)^2), (x, -oo, y))

Detail solution

Rewrite the integrand:

$\frac{1}{e^{\left(x - 1\right)^{2}}} = \frac{e^{2 x} e^{- x^{2}}}{e}$
The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{e^{2 x} e^{- x^{2}}}{e}\, dx = \frac{\int e^{2 x} e^{- x^{2}}\, dx}{e}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int e^{2 x} e^{- x^{2}}\, dx$
So, the result is: $\frac{\int e^{2 x} e^{- x^{2}}\, dx}{e}$
Add the constant of integration:

$\frac{\int e^{2 x} e^{- x^{2}}\, dx}{e}+ \mathrm{constant}$

The answer is:

$\frac{\int e^{2 x} e^{- x^{2}}\, dx}{e}+ \mathrm{constant}$

The answer (Indefinite) [src]

                        /  /            \    
  /                     | |             |    
 |                      | |    2        |    
 |      1               | |  -x   2*x   |  -1
 | ----------- dx = C + | | e   *e    dx|*e  
 |  /       2\          | |             |    
 |  \(x - 1) /          \/              /    
 | e                                         
 |                                           
/

$$\int \frac{1}{e^{\left(x - 1\right)^{2}}}\, dx = C + \frac{\int e^{2 x} e^{- x^{2}}\, dx}{e}$$

Simplify

The answer [src]

  ____     ____            
\/ pi    \/ pi *erf(-1 + y)
------ + ------------------
  2              2

$$\frac{\sqrt{\pi} \operatorname{erf}{\left(y - 1 \right)}}{2} + \frac{\sqrt{\pi}}{2}$$

  ____     ____            
\/ pi    \/ pi *erf(-1 + y)
------ + ------------------
  2              2

$$\frac{\sqrt{\pi} \operatorname{erf}{\left(y - 1 \right)}}{2} + \frac{\sqrt{\pi}}{2}$$

sqrt(pi)/2 + sqrt(pi)*erf(-1 + y)/2

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

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

Limits of integration:

The graph:

Piecewise:

The solution