anonymous
  • anonymous
Integrate (x+3)/(x-7)^2 using partial integration method?
Mathematics
katieb
  • katieb
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.Sam.
  • .Sam.
Partial fractions?
.Sam.
  • .Sam.
\[\frac{3+x}{(x-7)^2}=\frac{A}{x-7}+\frac{B}{(x-7)^2}\]
anonymous
  • anonymous
Yeah, it was partial fractions. My bad. lol

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.Sam.
  • .Sam.
So did you get it?
anonymous
  • anonymous
I knew how to do it up until this point but if you plug in 7, it gives you A(0) + B(0) = 10, so how do I find out the values of A and B separately?
anonymous
  • anonymous
Try values other than 7. Like x = 1 and 0, for convenience. This should give you a system of two equations with the unknowns, A and B.
anonymous
  • anonymous
I tried 6 and 8 and answer that I got is A=10 , B= 1. I hope that's correct
.Sam.
  • .Sam.
\[x+3=B+A (x-7)\] When x=7 B=10 When B has this value, when x=0, 0+3=10-7A A=1 \[\frac{x+3}{(x-7)^2}=\frac{1}{x-7}+\frac{10}{(x-7)^2}\]
.Sam.
  • .Sam.
Can you do it now? \[\int\limits \left(\frac{10}{(x-7)^2}+\frac{1}{x-7}\right) \, dx\]
anonymous
  • anonymous
yes. thank you for your help

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