Ok, so then when I find an LCD I get:
\int\sqrt{\frac{8(x+1)^4}{16(x+1)^4}+\frac{16(x+1)^8}{16(x+1)^4}+\frac{1}{16(x+1)^4}}
which simplifies to
\int\frac{4(x+1)^4 +1}{4(x+1)^2}
Is this as simple as possible? I'm afraid I still can't integrate this...
Find the exact length of the curve analytically by antidifferentiation:
y = (x3/3) + x2 + x + (1/(4x +4)) on the interval 0 < x < 2So I set it up using the length of a curve formula:
L = \int\sqrt{1+(x^2+2x+1+(\frac{-1}{4(x+1)^2}}
And simplified it to
L =...