Making a detour

Calculus Level 4

\[\int_C\frac{x}{(x^2+y^2)^{3/2}}dx+\frac{y}{(x^2+y^2)^{3/2}}dy\]

If \(C\) is the path defined by \(x=2^t\cos(2\pi t^2), y=2^t\sin(2\pi t^2)\), for \(0\leq t\leq 1\), find the integral above.

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