Question

Write a value of $\int \left(e^{x{\log }_{e}a}+e^{a{\log }_{e}x}\right)dx$.

Answer 1

$$\begin{gathered} \left(e^{x{\log }_{e}a}+e^{a{\log }_{e}x}\right)dx \\ \Rightarrow \int \left(e^{\log a^x}+e^{\log x^a}\right)dx \\ =\int \left(a^x+x^a\right)dx \\ =\frac{a^x}{\log a}+\frac{x^{a+1}}{a+1}+C \end{gathered}$$