I= ∫a^5x+3dx is:

The correct answer is Option (2) → $\frac{a^{5x+3}}{5\, log_ea}+C,$ where C is a constant

$I=∫a^{5x+3}dx$

let $5x+3=y$

$dy=5dx$

$I==\int\frac{a^y}{5}dy=\frac{a^y}{5\log a}+C$

$=\frac{a^{5x+3}}{5\log a}+C$