Question

\(\displaystyle \int 4^{x}\,dx=\) ?

• A. \(4^{x}+k\)
• B. \(\dfrac{4^{x+1}}{x+1}+k\)
• C. \(\dfrac{4^{x}}{\log 4}+k\)
• D. \(-\dfrac{4^{x}}{\log 4}+k\)

Hint:

Do not confuse with \(x^{n}\): that uses the power rule, not the exponential rule.

Answer 1

The Correct Option is C

For base \(a>0,\ a\ne1\): \(\displaystyle \int a^{x}dx=\frac{a^{x}}{\ln a}+C\). Putting \(a=4\) gives \(\dfrac{4^x}{\log 4}+k\) (here \(\log\) means natural log).