What is the integral of (x^2-8)/(x+3)dx

What is the integral of [(x^2-8)/(x+3)]dx? I've been stuck on this problem for a couple hours. I know it's something simple that is completely going over my head, but I really need it done by tonight. I already know what the answer is. Im not looking for the answer I'm looking how to solve the problem step by step. The answer to the problem is (x^2)/2 - 3x + ln|x+3| + C. The problem is supposed to be solved by trigonometric substitutions. I posted an image to show how the problem is supposed to look like. This is my failed attempt. Sorry if it looks messy, I wrote it not expecting to show anyone. Thanks

Calculus Integrals
Honeycrispalan Honeycrispalan
Matchmaticians What is the integral of (x^2-8)/(x+3)dx File #1 File #1 (jpeg)
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  • Honeycrispalan Honeycrispalan
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    Sorry I posted the wrong problem. The problem is actually the integral of [1/((4+x^2)^2)]dx

  • Honeycrispalan Honeycrispalan
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    Oh and it looks like I posted the wrong answer to the problem as well. Sorry my brain is feeling overwhelmed recently with all the math work. The answer to the problem is actually 1/16 arctan(x/2) + (x(4+x^2))/8 + C

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