MHB Did I make a mistake in evaluating this integral?

[shamieh]

Can someone check my work?$$
\int^4_0 \frac{6z + 5}{2z + 1} dz$$

$$\int^4_0 3 + \frac{2}{2z + 1} dz$$
$$
[3z + 2\ln|2z + 1|]^4_0 = 12 + 2\ln|9| $$

 

[lfdahl]

As far as I can see, you´ve done a great job - except for the factor 2 in front of ln|2z+1|

 

[shamieh]

the 2 cancels out with the 2z doesn't it? i think i see where i made my mistake

 

[Prove It]

the 2 cancels out with the 2z doesn't it? i think i see where i made my mistake

$\displaystyle \begin{align*} \int{\frac{1}{a\,x + b} \, dx} = \frac{1}{a} \ln{ \left| a \, x + b \right| } + C \end{align*}$