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

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, $e \approx 2.71828$.