Final Answer
$377.453095$
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Step-by-step Solution
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1
Rewrite the integrand $\left(5e^x+3\right)^3$ in expanded form
$\int_{\frac{57}{200}}^{0.585}\left(125e^{3x}+225e^{2x}+135e^x+27\right)dx$
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$\int_{\frac{57}{200}}^{0.585}\left(125e^{3x}+225e^{2x}+135e^x+27\right)dx$
Learn how to solve problems step by step online. Integrate the function (5e^x+3)^3 from 57/200 to 0.585. Rewrite the integrand \left(5e^x+3\right)^3 in expanded form. Expand the integral \int_{\frac{57}{200}}^{0.585}\left(125e^{3x}+225e^{2x}+135e^x+27\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{\frac{57}{200}}^{0.585}125e^{3x}dx results in: 143.003057. The integral \int_{\frac{57}{200}}^{0.585}225e^{2x}dx results in: 163.544129.
Final Answer
$377.453095$