Question

Write a value of

\[\int e^{3 \text{ log x}} x^4\text{ dx}\]

Answer 1

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