How Do You Solve the Integral of (1-e^-x)^(1/2)?

[osy044]

Homework Statement

what is the integral of (1-e^-x)^(1/2)?
HELP~~

Homework Equations

The Attempt at a Solution

 

[ehild]

What do you think about the substitution t^2=1-e^(-x)= ?

ehild

 

[CompuChip]

I think it is
$$\frac{\sqrt{1-e^{-x}} \left(e^{x/2} x-2 \sqrt{e^x-1}+2 e^{x/2} \log<br /> \left(-e^{-x/2} \sqrt{e^x-1}-1\right)\right)}{\sqrt{e^x-1}}$$

Is that what you got as well?

By the way, I find this a rather hard calculus problem for an introductory physics class.

 

[ehild]

I think it is
$$\frac{\sqrt{1-e^{-x}} \left(e^{x/2} x-2 \sqrt{e^x-1}+2 e^{x/2} \log<br /> \left(-e^{-x/2} \sqrt{e^x-1}-1\right)\right)}{\sqrt{e^x-1}}$$

Is that what you got as well?

By the way, I find this a rather hard calculus problem for an introductory physics class.

I was too lazy to check either formula. I left e^-x unchanged, used the substitution 1-e^-x =t²,

$$dx=\frac{2tdt}{1-t^2}$$

I also got the logarithm of a fraction plus a constant times the square root. The problem can be solved, and you are right, it should rather be at "Calculus and Beyond"

ehild