Happy Birthday, Mehul!

Calculus Level 3

115exsinh(x)dx\large\int\limits_{1}^{15} e^x\sinh(x) \,\mathrm dx

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

Clarification: ee denotes the Euler's number, e2.71828e \approx 2.71828 .

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

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