1. log derivatives

can someone check if I'm doing this right:

1.) $\displaystyle \frac{d}{dx} \int^{3x+2}_1 \frac{1}{t}dt$

$\displaystyle \frac{d}{dx} ln(3x+2)$

$\displaystyle \frac{1}{3x+2}*3$

ans: $\displaystyle \frac{3}{3x+2}$
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2.) $\displaystyle \int\big(\frac{d}{dx} lnf(x)\big)dx$

$\displaystyle \int \frac{1}{f(x)}dx$

ans: $\displaystyle lnf(x) + C$

2. Originally Posted by viet
can someone check if I'm doing this right:

1.) $\displaystyle \frac{d}{dx} \int^{3x+2}_1 \frac{1}{t}dt$

$\displaystyle \frac{d}{dx} ln(3x+2)$

$\displaystyle \frac{1}{3x+2}*3$

ans: $\displaystyle \frac{3}{3x+2}$
This looks correct to me, even after I had 6 shots of whiskey. What was I saying again?
2.) $\displaystyle \int\big(\frac{d}{dx} lnf(x)\big)dx$

$\displaystyle \int \frac{1}{f(x)}dx$

ans: $\displaystyle lnf(x) + C$
But no need to do all that.
You should not that the integral of the derivative is the original function plus constants. Since the original function was $\displaystyle \ln f(x)$ means the the answer would be $\displaystyle \ln f(x) +C$.

3. the 2nd question

Originally Posted by viet
can someone check if I'm doing this right:

2.) $\displaystyle \int\big(\frac{d}{dx} lnf(x)\big)dx$

$\displaystyle \int \frac{1}{f(x)}dx$

ans: $\displaystyle lnf(x) + C$
On the 2nd question