$\huge \begin{align} f'''(x) &= e^{x} \\ f''(0)&= 2 \\ f'(0)&=7\\ f(x) &= \int_{0}^x \pa{6+ \int_{0}^{x}\pa{ 1+\int_{0}^{x} e^x\d x} \d x}\d x\\ &= 6x+ \frac{1}{2} x^2+e^x +C \end{align}$