Question:
\(\displaystyle \int 4^{x}\,dx=\) ?
\(\displaystyle \int 4^{x}\,dx=\) ?
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Do not confuse with \(x^{n}\): that uses the power rule, not the exponential rule.
Updated On: Oct 17, 2025
- \(4^{x}+k\)
- \(\dfrac{4^{x+1}}{x+1}+k\)
- \(\dfrac{4^{x}}{\log 4}+k\)
- \(-\dfrac{4^{x}}{\log 4}+k\)
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The Correct Option is C
Solution and Explanation
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).
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