Given that int_{1}^{3} e^{x} d x=e^{3}-e, use this result to evaluate int_{1}^{3} 5 e^{x+4} d x

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Step:1 ：The given integral is (int_{1}^{3} e^{x} d x = e^{3}-e). We need to evaluate (int_{1}^{3} 5 e^{x+4} d x).Step:2 ：We can rewrite the integral (int_{1}^{3} 5 e^{x+4} d x) as (int_{1}^{3} 5 e^{x} e^{4} d x), which simplifies to (5e^{4}int_{1}^{3} e^{x} d x).Step:3 ：Substituting the given integral (int_{1}^{3} e^{x} d x = e^{3}-e) into the equation, we get the final answer.Step:4 ：Thus, the value of the integral (int_{1}^{3} 5 e^{x+4} d x) is (boxed{4741.09999662941}).

Answer

Step: 1 ：The given integral is (int_{1}^{3} e^{x} d x = e^{3}-e). We need to evaluate (int_{1}^{3} 5 e^{x+4} d x).Step: 2 ：We can rewrite the integral (int_{1}^{3} 5 e^{x+4} d x) as (int_{1}^{3} 5 e^{x} e^{4} d x), which simplifies to (5e^{4}int_{1}^{3} e^{x} d x).Step: 3 ：Substituting the given integral (int_{1}^{3} e^{x} d x = e^{3}-e) into the equation, we get the final answer.Step: 4 ：Thus, the value of the integral (int_{1}^{3} 5 e^{x+4} d x) is (boxed{4741.09999662941}).

Given that $\int_{1}^{3} e^{x} d x=e^{3}-e$, use this result to evaluate $\int_{1}^{3} 5 e^{x+4} d x$

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