A question about beginning integration.

Question

$$F(x)=\int_{3}^{x} \frac{1}{\ln(3t)}dt$$ for $x \ge 3$.On what intervals in $F$ increasing? I am trying to edit it so I can get my ban lifted. What should I have asked? I didn't understand the fundamentals of calculus when I asked it.

Answer 1

It is increasing on any interval, since $F'(x)=\frac1{\log(3x)}>0$.

Answer 2

The graph of $$\frac1{\ln(3t)}$$ is greater than $0$ for all $t$ in the integration range - from $3$ to $x$. When you integrate, you are computing the area under the curve. Since the curve is above the $x$ axis, this means that as you increase $x$, (i.e. increase the range of integration) you increase the area under the curve, and so $F(x)$ increases. So $F$ is increasing on any interval.