Write a value

Question:

Write a value of $\int e^{3 \log x} x^{4} d x$.

Solution:

Consider $\int e^{3 \log x} x^{4}$

$e^{3 \log x}=e^{\log x^{3}}$

$=x^{3}$

$\int e^{3 \log x} x^{4}=\int x^{3} x^{4} d x$

$=\int x^{7} d x$

$=\frac{x^{8}}{8}+c$

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