TITLE: Evaluate the Integral: $\int\frac{3t-2}{t+1}$
QUESTION [1 upvotes]: Evaluate the Integral: $\int\frac{3t-2}{t+1}$
1) Long division gives $\int3-\frac{5}{t+1}dt$
2)I take the negative and constant outside of the integral. 
$-3\int\frac{5}{t+1}dt$
3) I then take the 5 out side the integral and multiply it by the three. 
$-15\int\frac{1}{t+1}dt$
4) U-substitution 
$u=t+1$ and $du=dt$
5) Integrate
$-15\ln|t|+C$
6) Replace $u$ with $t+1$
Final answer is $-15\ln|t+1|+C$
Am I correct if not please explain.

REPLY [1 votes]: \begin{align*}
\int \left(3-\frac{5}{t+1}\right)\,dt&=\int 3\,dt-\int \frac{5}{t+1}\,dt\\
&=3t-5\ln|t+1|+C
\end{align*}
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