Question

If \[ \int\frac{e^x+3}{\sqrt{e^x+4}}\,dx = 2\sqrt{e^x+4} +\frac32 \log\left| \frac{f(x)-2}{f(x)+2} \right| +c \] and \[ f(0)=\sqrt5, \] then \[ f(\log_e5)= \]

• A. \(\sqrt5\)
• B. \(2\)
• C. \(3\)
• D. \(\sqrt7\)

Hint:

Remember, \[ \boxed{ e^{\log_e a}=a. } \] Also, compare the given integral with the obtained result to identify the unknown function.

Answer 1

The Correct Option is C