$\int a^{x}\,dx$ (with $a0,\ a
eq 1$) equals

Question

$\int a^{x}\,dx$ (with $a>0,\ a
eq 1$) equals

Accepted Answer

C. $\dfrac{a^{x}}{\log a}+C$

1. From the standard list, $\dfrac{d}{dx}\left(\dfrac{a^{x}}{\log a}\right)=a^{x}$.
2. Therefore $\int a^{x}\,dx=\dfrac{a^{x}}{\log a}+C$.
3. Option A is the derivative, not the integral.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.290_

Answer

$a^{x}\log a+C$

Answer

$x\,a^{x-1}+C$

Answer

$\dfrac{a^{x+1}}{x+1}+C$

$\int a^{x}\,dx$ (with $a>0,\ a\neq 1$) equals