After working with some parametric equations, I have arrived to the following integral that describes arc length.
$$\int \sqrt{\frac{9x^{12} + 10000x^8 - 1080x^6 + 32400}{10000x^8}}dx$$
Using by parts integration doesn't seem to work.
I seem to have lost the starting values for f(x) and g(x), but they were something along the lines of:
$$f(x)=x$$ and $$g(x)=\frac{x^3}{100}+\frac{6}{10x^3}$$
Thanks in advance.