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Math Help - Integrating this problem

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by larryboi7 View Post
    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.
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  3. #3
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    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?

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  4. #4
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    thank you so much that really helped me
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