Question

\( \int \left(e^{x\log_e 6}\right)e^x dx = \phi(x) + c \) then \( \phi(x) = \)

• A. \( 6^x e^x \)
• B. \( \frac{e^x}{\log 6e} \)
• C. \( \frac{6^x}{1+\log_e 6} \)
• D. \( \frac{(6e)^x}{1+\log_e 6} \)

Hint:

Use identity \( e^{x\ln a} = a^x \) to simplify exponential integrals quicklyThen apply standard \( \int a^x dx \) formula.

Answer 1

The Correct Option is D