Question

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

Answer 1

$$\begin{gathered} \int e^{3\log x}.x^{4}dx \\ =\int e^{\log x^3}·x^{4}dx\left(\because a\log x=\log x^a\right) \\ =\int x^3·x^{4}dx\left(\because e^{\log m}=m\right) \\ =\int x^7·dx \\ =\frac{x^8}{8}+C \end{gathered}$$