Happy Birthday, Mehul!

Calculus Level 3

\[\large\int\limits_{1}^{15} e^x\sinh(x) \,\mathrm dx\]

If the above integral has a closed form: \(\dfrac{a-e^b+e^c}{d}\) for some integers \(a,b,c,d\) where \(a<0\) , then find the value of \(a+b+c+d\) .

Clarification: \(e\) denotes the Euler's number, \(e \approx 2.71828 \).


This problem is original and is dedicated to Mehul on his birthday.
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