Question: Find the length of the curve for spiral \(r={{e}^{3\theta }}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}0\le \theta \le \pi \)

\(\frac{1}{12}({{e}^{6\pi }}-1)_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}\frac{\sqrt{10}}{3}({{e}^{3\pi }}-1)_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}8({{\pi }^{2}}-1)_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}_{{}}^{{}}{{e}^{6\pi }}-\sqrt{3}\)

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