# Thread: Second Fundamental Theorem of Calculus

1. ## Second Fundamental Theorem of Calculus

Hello! I am stuck on this problem. I have tried lots of things, but just can't seem to get the right answer. Thanks for your help!

2. $\ln(3x)=\ln3+\ln x,$ can you proceed?

3. I tried substituting that in for ln(3x), but I'm still getting the wrong answer. Could you help me out with some more steps? Thanks!

4. Originally Posted by jsl
I tried substituting that in for ln(3x), but I'm still getting the wrong answer. Could you help me out with some more steps? Thanks!
Let $u=\ln3x$, then $du=\frac{3}{3x}dx=\frac{1}{x}dx$

Now Note that $\int\frac{\ln3x}{x}dx=\int(\ln3x)\left(\frac{1}{x} \right)dx$

So, we make the substution

$\int(u)du$