# Evaluate the Integral

#### shamieh

##### Active member
Can someone check my work?

$$\displaystyle \int^4_0 \frac{6z + 5}{2z + 1} dz$$

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

#### lfdahl

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

#### shamieh

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

#### Prove It

##### Well-known member
MHB Math Helper
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*}