1. ## anti-derivatives

sorry for multiple posts today, i'm studying for my calc final and just wanna make sure i know the correct order of solving these.

"solve the anti-derivative"
$\displaystyle f(x) = \frac{1}{x}(lnx + 3)$

do i solve them separately? or distribute the $\displaystyle \frac{1}{x}$?

2. Originally Posted by JGaraffa
sorry for multiple posts today, i'm studying for my calc final and just wanna make sure i know the correct order of solving these.

"solve the anti-derivative"
$\displaystyle f(x) = \frac{1}{x}(lnx + 3)$

do i solve them separately? or distribute the $\displaystyle \frac{1}{x}$?
Well, again, use substitution $\displaystyle z := \ln x+3$, which gives you that $\displaystyle dz = \tfrac{1}{x}\,dx$ and hence

$\displaystyle \int \tfrac{1}{x}(\ln x+3)\, dx=\int z\, dz=\ldots$

3. got it, thanks man.

i just posted a reply in the other thread "definite integral" which you responded to, i'm still a little confused if i'm solving it right (the numbers came out really high) if you could just check it out that would be great.

4. Originally Posted by JGaraffa
sorry for multiple posts today, i'm studying for my calc final and just wanna make sure i know the correct order of solving these.

"solve the anti-derivative"
$\displaystyle f(x) = \frac{1}{x}(lnx + 3)$

do i solve them separately? or distribute the $\displaystyle \frac{1}{x}$?
Again observe that $\displaystyle 1/x$ is the derivative of $\displaystyle \ln(x)+3$ so what is the derivative of:

$\displaystyle (\ln(x)+3)^2$ ?

CB