Integration of (e[SUP]-√x[/SUP])/√x

[Anne5632]

Homework Statement

Compute the integral with upper bound infinity and lower bound 1

Relevant Equations

Integral of (e[SUP]-√x[/SUP])/√x

(e^-√x)/√x (integral from title)

I integrated by substituting and the bounds changed with inf changing to -inf and 1 changing to -1

My final integrated answer is -2lim[e^-√x]. What happens to this equation at -inf and -1? As I can't put them into the roots

 

[PeroK]

I'm not sure I understand the difficulty.

 

[pasmith]

Homework Statement:: Compute the integral with upper bound infinity and lower bound 1
Relevant Equations:: Integral of (e^-√x)/√x

(e^-√x)/√x (integral from title)

I integrated by substituting and the bounds changed with inf changing to -inf and 1 changing to -1

My final integrated answer is -2lim[e^-√x]. What happens to this equation at -inf and -1? As I can't put them into the roots

You have the wrong limits. $\sqrt{x}$ is the positive root. Thus $\sqrt{1} = 1$ and $\sqrt{+\infty} = +\infty$.

 

[Anne5632]

You have the wrong limits. $\sqrt{x}$ is the positive root. Thus $\sqrt{1} = 1$ and $\sqrt{+\infty} = +\infty$.

Thank you, I originally let my substitution = -√x
But √x is better
Final answer now is 2/e