# Use a table of integrals to evaluate the following integrals. int x^(2)e^(5x)dx

daniko883y 2022-10-01 Answered
Use a table of integrals to evaluate the following integrals. $\int {x}^{2}{e}^{5x}dx$
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## Answers (1)

Garrett Valenzuela
Answered 2022-10-02 Author has 9 answers
From the Table of Integrals:
$\int {x}^{2}{e}^{ax}dx=\left(\frac{{x}^{2}}{a}-\frac{2x}{{a}^{2}}+\frac{2}{{a}^{3}}\right){e}^{ax}+C$
Therefore:
$\int {x}^{2}{e}^{5x}dx=\left(\frac{{x}^{2}}{5}-\frac{2x}{25}+\frac{2}{125}\right){e}^{5x}+C$
Result:
$\left(\frac{{x}^{2}}{5}-\frac{2x}{25}+\frac{2}{125}\right){e}^{5x}+C$
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