# integration

• February 24th 2009, 08:21 AM
jarny
integration
Hello,

I am having trouble integrating the following equation, I thought I could do it but it is not the same as the answer in the back of the book. Can someone help me?

The integral of (2x+3)/(x+1)dx thanks
• February 24th 2009, 08:37 AM
Reckoner
Quote:

Originally Posted by jarny
Hello,

I am having trouble integrating the following equation, I thought I could do it but it is not the same as the answer in the back of the book. Can someone help me?

The integral of (2x+3)/(x+1)dx thanks

$\int\frac{2x+3}{x+1}\,dx$

$=\int\frac{2x+2+1}{x+1}\,dx$

$=\int\frac{2(x+1)+1}{x+1}\,dx$

$=\int\left[\frac{2(x+1)}{x+1}+\frac1{x+1}\right]dx$

$=\int\left(2+\frac1{x+1}\right)dx$

You could have also used polynomial long division.
• February 24th 2009, 08:38 AM
janvdl
Quote:

Originally Posted by jarny
Hello,

I am having trouble integrating the following equation, I thought I could do it but it is not the same as the answer in the back of the book. Can someone help me?

The integral of (2x+3)/(x+1)dx thanks

$\int{\frac{2x+3}{x+1}} dx$

$= 2 \int{ \frac{x}{x+1} }dx + 3 \int{ \frac{1}{x+1} }dx$

$= 2 \int{ \frac{x+1-1}{x+1} }dx + 3 \ln{(x+1)} + C$

$
= 2 \left( \int{ \frac{x+1}{x+1} }dx + \int{ \frac{-1}{x+1} }dx \right) + 3 \ln{(x+1)} + C$

$= 2 \left( \int{ 1 }dx + \int{ \frac{-1}{x+1} }dx \right) + 3 \ln{(x+1)} + C$

$= 2 \left( x - \ln{(x+1)} \right) + 3 \ln{(x+1)} + C$

$= 2x + \ln{(x+1)} + C$
• February 24th 2009, 10:19 AM
Krizalid
Of course janvdl meant to say $\ln|x+1|.$ :)
• February 24th 2009, 10:33 AM
jarny
thanks a lot guys
• February 25th 2009, 01:49 AM
janvdl
Quote:

Originally Posted by Krizalid
Of course janvdl meant to say $\ln|x+1|.$ :)

I even wrote it like that on the paper I worked it out on... Sorry about that. (Speechless)