# anti-derivatives

• May 4th 2010, 11:08 AM
JGaraffa
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 $\displaystyle \frac{1}{x}$?
• May 4th 2010, 11:13 AM
Failure
Quote:

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

$\displaystyle \int \tfrac{1}{x}(\ln x+3)\, dx=\int z\, dz=\ldots$
• May 4th 2010, 11:36 AM
JGaraffa
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.
• May 4th 2010, 11:24 PM
CaptainBlack
Quote:

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