Evaluate $\int_{-3}^{1} e^{3 x}+9 x^{2}-8 d x$

Step 1 ：Evaluate \(\int_{-3}^{1} e^{3 x}+9 x^{2}-8 d x\)

Step 2 ：Integrate each term separately: \(\int e^{3x} dx = \frac{1}{3}e^{3x}\), \(\int 9x^2 dx = 3x^3\), \(\int -8 dx = -8x\)

Step 3 ：Evaluate the resulting expression from -3 to 1: \(\left[\frac{1}{3}e^{3x} + 3x^3 - 8x\right]_{-3}^{1}\)

Step 4 ：Substitute the limits of integration: \(\left[\frac{1}{3}e^{3(1)} + 3(1)^3 - 8(1)\right] - \left[\frac{1}{3}e^{3(-3)} + 3(-3)^3 - 8(-3)\right]\)

Step 5 ：Simplify the expression: \(-\frac{1}{3}e^{-9} + \frac{1}{3}e^{3} + 52\)

Step 6 ：Calculate the final result: \(58.6951378377945\)

Step 7 ：Final Answer: \(\boxed{58.695}\)