How Do You Solve the Integral of e^(-x^2+2x) from 1 to Infinity?

[imana41]

hi pleaes help me about this
[URL]http://latex.codecogs.com/gif.latex?\int_{1}^{\infty%20}e^{-x^2+2x}dx[/URL]

i know the [URL]http://latex.codecogs.com/gif.latex?\int_{0}^{\infty%20}e^{-x^2}dx[/URL] is [URL]http://latex.codecogs.com/gif.latex?\sqrt{%20pi}/2[/URL]
but can't solve above integral !?

 

[mahdisadjadi]

Rewrite the power as:
$$-x^{2}+2x=-(x-1)^2+1$$
It we define x-1=t,
$$-x^{2}+2x=-t^2+1$$
so
$$e^{-x^{2}+2x}=e^{-t^2+1}=e^{-t^2}e^{1}$$
and we also know that dx=dt, change the variable of integral and enjoy!

 

[imana41]

thanks the the answer of integral is