Integration Mania

Calculus Level 4

\[ \displaystyle \int_{\frac{\pi}{4}}^{\frac{\pi}{3}} e^x \left ( \frac{2+\sin(2x)}{1 + \cos(2x)} \right) \, dx \]

If the integral above can be expressed as \( \large e^{\frac{\pi}{a}} ( be^{\frac{\pi}{c}} - d) \), evaluate \( \dfrac{ b^2 c}{ad^{10} } \).

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