# Math Help - Integrating this problem

1. ## Integrating this problem

how do i integrate the problem:

\int (x^2+2x+1)/(2x+3) dx

I'm so stuck on this

Thank You

2. Originally Posted by larryboi7
how do i integrate the problem:

\int (x^2+2x+1)/(2x+3) dx

I'm so stuck on this

Thank You
Do the long division.

3. Hello, larryboi7!

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

Note that the numerator is a quadratic, the denominator is linear.
. . The fraction is "improper".

Use long division: . $(x^2+2x+1) \div (2x+3) \;=\;\frac{1}{2}\,x + \frac{1}{4} + \frac{\frac{1}{4}}{2x+3}$

The integral becomes: . $\int\left(\frac{1}{2}\,x + \frac{1}{4} + \frac{1}{4}\!\cdot\!\frac{1}{2x+3}\right)dx \;=\;\frac{1}{2}\!\int\! x\,dx + \frac{1}{4}\!\int\! dx + \frac{1}{4}\!\int\!\frac{dx}{2x+3}$

And you can finish it, right?

4. thank you so much that really helped me