# Thread: Trouble with integration (trig. inverse forms)

1. ## Trouble with integration (trig. inverse forms)

Here is the link from wolframalpha:
integral (1/[(e^(4x) -36)^(1/2)])dx - Wolfram|Alpha

I understand what W.A. did, but i think there should be an easier way than making so many substitutions.
I would appreciate hints, don't solve it entirely.

Thanks.

2. Originally Posted by Arturo_026
Here is the link from wolframalpha:
integral (1/[(e^(4x) -36)^(1/2)])dx - Wolfram|Alpha

I understand what W.A. did, but i think there should be an easier way than making so many substitutions.
I would appreciate hints, don't solve it entirely.
Since the denominator is of the form

$\displaystyle \sqrt{y^2-6^2}$

This suggests the trig sub $\displaystyle y=6\sec{t}$ but $\displaystyle y=e^{2x}$ so you get

$\displaystyle e^{2x}=6\sec{t}$

This will combine all the substituions that WA did into one step
Thanks.

3. Thanks, but I haven't been thought that or seen a similar method. This problem is from a chapter on inverse trigonometric and hyperbolic functions. (or perhaps just inverses, logs, and exponoential).
-Thanks

4. I finally figured it out.!!! By timing top and bottom by e^(2x) i get the sec inverse form.
Thanks for the help