Evaluate the definite integral: $$ \int_{0}^{1} \frac{2 e^{8 x}-5}{e^{3 x}} d x=\square $$

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Calculate the integral $$ \int_{0}^{1} \frac{2 e^{8x}-5}{e^{3x}} dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using substitution:
  $$\int_{0}^{1} \frac{2e^{8x}-5}{e^{3x}} dx$$
- step1: Simplify the expression:
  $$\int_{0}^{1} \left(2e^{8x}-5ight)e^{-3x} dx$$
- step2: Evaluate the integral:
  $$\int \left(2e^{8x}-5ight)e^{-3x} dx$$
- step3: Use the substitution $$dx=-\frac{e^{3x}}{3} dt$$ to transform the integral$$:$$
  $$\int \left(2e^{8x}-5ight)e^{-3x}\left(-\frac{e^{3x}}{3}ight) dt$$
- step4: Simplify:
  $$\int -\frac{\left(2e^{-3x}	imes e^{8x}-5e^{-3x}ight)e^{3x}}{3} dt$$
- step5: Use the substitution $$t=e^{-3x}$$ to transform the integral$$:$$
  $$\int -\frac{\left(2t\left(e^{-\frac{1}{3}\ln{\left(tight)}}ight)^{8}-5tight)t^{-1}}{3} dt$$
- step6: Simplify:
  $$\int -\frac{2t^{-\frac{5}{3}}-5t}{3t} dt$$
- step7: Rewrite the expression:
  $$\int -\frac{1}{3}	imes \frac{2t^{-\frac{5}{3}}-5t}{t} dt$$
- step8: Use properties of integrals:
  $$-\frac{1}{3}	imes \int \frac{2t^{-\frac{5}{3}}-5t}{t} dt$$
- step9: Rewrite the fraction:
  $$-\frac{1}{3}	imes \int \left(-5+\frac{2}{t^{\frac{8}{3}}}ight) dt$$
- step10: Use properties of integrals:
  $$-\frac{1}{3}\left(\int -5 dt+\int \frac{2}{t^{\frac{8}{3}}} dtight)$$
- step11: Calculate:
  $$-\frac{1}{3}	imes \int -5 dt-\frac{1}{3}	imes \int \frac{2}{t^{\frac{8}{3}}} dt$$
- step12: Evaluate the integral:
  $$\frac{5}{3}t-\frac{1}{3}	imes \int \frac{2}{t^{\frac{8}{3}}} dt$$
- step13: Evaluate the integral:
  $$\frac{5}{3}t+\frac{2}{5t^{\frac{5}{3}}}$$
- step14: Substitute back:
  $$\frac{5}{3}e^{-3x}+\frac{2}{5\left(e^{-3x}ight)^{\frac{5}{3}}}$$
- step15: Evaluate the power:
  $$\frac{5}{3}e^{-3x}+\frac{2}{5e^{-5x}}$$
- step16: Simplify the expression:
  $$\frac{5}{3}e^{-3x}+\frac{2e^{5x}}{5}$$
- step17: Multiply the terms:
  $$\frac{5}{3e^{3x}}+\frac{2e^{5x}}{5}$$
- step18: Return the limits:
  $$\left(\frac{5}{3e^{3x}}+\frac{2e^{5x}}{5}ight)\bigg |_{0}^{1}$$
- step19: Calculate the value:
  $$\frac{25+6e^{8}-31e^{3}}{15e^{3}}$$
The definite integral $$ \int_{0}^{1} \frac{2 e^{8 x}-5}{e^{3 x}} d x $$ evaluates to $$ \frac{25+6e^{8}-31e^{3}}{15e^{3}} $$.
The definite integral $$ \int_{0}^{1} \frac{2 e^{8x}-5}{e^{3x}} dx $$ equals $$ \frac{25 + 6e^{8} - 31e^{3}}{15e^{3}} $$.

Evaluate the definite integral:

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