Question

`∫a^(3x+2) dx` is equal to ______.

Options

• `(a^(3x)/(3log_ea)) + c`

• `a^2x + (a^(3x)/(3log_ea)) + c`

• `a^2(a^(3x)/(3log_ea)) + c`

• `a^2(a^(3x)/(log_ea)) + c`

Answer 1

`∫a^(3x+2) dx` is equal to `bbunderline(a^2(a^(3x)/(3log_ea)) + c)`.

Explanation:

Given that,

= ∫a^3x+2dx

= a²∫a^3x . a² . dx

= a²∫a^3xdx

= `a^2(a^(3x)/(3log_ea)) + c          ...[∵ ∫a^x = a^x/log_ea + c]`

Option `a^2(a^(3x)/(3log_ea)) + c` is correct.