Question

Write a value of\[\int\left( e^{x \log_e \text{  a}} + e^{a \log_e x} \right) dx\] .

Answer 1

\[\left( e^{\text{ x   log}_e a} + e^{\text{ a }\log_e x} \right)dx\]
\[\int\left( e^{ \text{ log a}^x} + e^{ \text{ log x}^a} \right) dx\]
\[ = \int \left( a^x + x^a \right)dx\]
\[ = \frac{a^x}{\log a} + \frac{x^{a + 1}}{a + 1} + C\]