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Question
Write a value of
\[\int e^{3 \text{ log x}} x^4\text{ dx}\]
Sum
Solution
\[\int e^{3 \text{ log x}} . x^4 \text{ dx }\]
\[ = \int e^{\text{ log x}^3} \cdot \text{ x}^4\text{ dx } \left( \because a\log x = \log x^a \right)\]
\[ = \int x^3 \cdot x^4 \text{ dx } \left( \because e^{\text{ log m}} = m \right)\]
\[ = \int x^7 \cdot dx\]
\[ = \frac{x^8}{8} + C\]
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