# Double exponential integration (a,∞) - how to implement.

1. Mar 28, 2014

### maistral

NOTE: This isn't homework.

So I'm trying to integrate a really awkward integral with limits from a to infinity;

$\int^{∞}_{30471.2729807}(\frac{83.1451 * 373.15}{X})-(\frac{83.1451 * 373.15}{X-30.4811353}-\frac{5534906.5380409}{X^2})dX$

Since the Simpson's and Trapezoidal would be really awkward to use with these (I literally used a limit of 30471.2729807 to 1000000000 (lol)) I tried to search for other alternatives, and I found this.

I can't understand how this is implemented though. This transformation

$\int^{∞}_{a}f(X)dX → \int^{∞}_{0}f(X+a)dX$

is bothering me as well. Can someone point me where a step-by-step algorithm of the method's implementation is made; or if possible, someone tell me how it was done?

2. Mar 28, 2014

### UltrafastPED

It's a transformation of variables: let u=X+a; then for X=(a,inf) we get u=(0,inf), and dX = du.

All they did was skip the formal analysis and went directly to the result: f(u) = f(X+a).

3. Mar 28, 2014

### maistral

I see. Got it.

4. Mar 28, 2014

### SteamKing

Staff Emeritus