# Exponential integral

1. Aug 14, 2010

### k_c

1. The problem statement, all variables and given/known data

I'm working out different pathlengths for different solids but I'm stuck on the following integral:

2. Relevant equations

$$\int$$ x*exp(-C*sqrt[1-x2/A2]) dx

exp = exponential func
sqrt = square root
C and A are constants

3. The attempt at a solution

I tried to work it out with the substitution method, where u = -C*sqrt[1-x2/A2] and du = C/A2x(1-x2/A2)-1/2.

But it seems to be getting really complex afterwards, so I was wondering if I'm overlooking the simple approach for this integral?

2. Aug 15, 2010

### Whitishcube

try integration by parts.

3. Aug 15, 2010

### k_c

I tried it this way now:

u^2 = (1-x^2/a^2)
so du = -2x/a^2 dx and therefore x dx = -a^2/2 du

So the integral becomes: $$\int$$ -a^2/2 exp^(-cu) du
And then i find the solution: a^2/(2c) exp^(-cu)

Which is a^2/(2c) exp^[-c sqrt(1-x^2/a^2)]

I think this should be correct but the wolfram mathematica integrator gives me a different solution, so if somebody could confirm my method/solution, that would be great..

4. Aug 15, 2010

### ehild

Check du.

ehild

5. Aug 15, 2010

### hunt_mat

For the integral:
$$\int x\exp (-c\sqrt{1-x^{2}/a^{2}})dx$$
I use the substitute:
$$u^{2}=1-\frac{x^{2}}{a^{2}}$$
Then:
$$xdx=a^{2}udu$$
This makes the integral become:
$$a^{2}\int ue^{-u}du$$
This I think is easy to compute, so I will leave that part to you.