Having Trouble Finding The Length Of A Parametric Curve

Hey everyone. I've been trying to find the length of this parametric curve, but haven't had much luck.

After finding and and substituting them into the formula for curve length, I got:

After this, I tried u-substitution, but couldn't figure out how to eliminate the resultant :

I consulted Wolfram Alpha as a last result, but couldn't figure out how they got the

Help would be greatly appreciated!

Re: Having Trouble Finding The Length Of A Parametric Curve

Multiply top and bottom by the conjugate.

Re: Having Trouble Finding The Length Of A Parametric Curve

Hello, Algebrah!

We have: .

Re: Having Trouble Finding The Length Of A Parametric Curve

Re: Having Trouble Finding The Length Of A Parametric Curve

Sorry, I turned off my computer last night and then proceeded to solve the problem using the conjugate method.

I also really appreciate Soroban's method, which is a nice use of the power-reducing formula.

Thanks a lot for the help!