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Solving integrals/ exp(x^2-4x+A)

Integral of exp(x^2-4x+A) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |    2             
 |   x  - 4*x + a   
 |  e             dx
 |                  
/                   
0
$$\int\limits_{0}^{1} e^{a + \left(x^{2} - 4 x\right)}\, dx$$ 
Integral(exp(x^2 - 4*x + a), (x, 0, 1))
Detail solution

    ErfRule(a=1, b=-4, c=a, context=exp(a + x**2 - 4*x), symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 |   2                      ____               -4 + a
 |  x  - 4*x + a          \/ pi *erfi(-2 + x)*e      
 | e             dx = C + ---------------------------
 |                                     2             
/
$$\int e^{a + \left(x^{2} - 4 x\right)}\, dx = C + \frac{\sqrt{\pi} e^{a - 4} \operatorname{erfi}{\left(x - 2 \right)}}{2}$$
Simplify
The answer [src] 
  ____          -4  a     ____          -4  a
\/ pi *erfi(2)*e  *e    \/ pi *erfi(1)*e  *e 
--------------------- - ---------------------
          2                       2
$$- \frac{\sqrt{\pi} e^{a} \operatorname{erfi}{\left(1 \right)}}{2 e^{4}} + \frac{\sqrt{\pi} e^{a} \operatorname{erfi}{\left(2 \right)}}{2 e^{4}}$$ 
=
= 
  ____          -4  a     ____          -4  a
\/ pi *erfi(2)*e  *e    \/ pi *erfi(1)*e  *e 
--------------------- - ---------------------
          2                       2
$$- \frac{\sqrt{\pi} e^{a} \operatorname{erfi}{\left(1 \right)}}{2 e^{4}} + \frac{\sqrt{\pi} e^{a} \operatorname{erfi}{\left(2 \right)}}{2 e^{4}}$$ 
sqrt(pi)*erfi(2)*exp(-4)*exp(a)/2 - sqrt(pi)*erfi(1)*exp(-4)*exp(a)/2

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

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