Date: Aug 19, 2011 3:36 PM
Author: Oscarville
Subject: Difficult Integral

Hi. I have an integral which I cannot solve.

Integrate: [(e^t) + (t^2) + 1]^1/2

That's the general look of it. Wolfram Alpha reported: Indefinite Integral: (no result found in terms of standard mathematical functions)

It did however report a series expansion of the integral at t = 0.

So, I'm trying to suggest a formula for the arc length of a three dimensional curve. I've identified the parameters and explicated it towards the arc length formula in three dimensions. All seemed to be going smooth until I reached this point. As the variable (t) shows up on top of e as well as a regular "number", raised to the power 2, I'm at a total loss as to how this integral might be solved. I'm also fuzzy on what the series expansion might have to offer in terms of yielding an arc length value from t=0 to whatever I desire (but I will look into that further).

It would be nice to find an equation for this. If anyone has any suggestions or tips on how to approach this integral I would be very grateful. Thanks