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mathematics44

  • 2 years ago

Integrate (x+3)/(x-7)^2 using partial integration method?

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  1. .Sam.
    • 2 years ago
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    Partial fractions?

  2. .Sam.
    • 2 years ago
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    \[\frac{3+x}{(x-7)^2}=\frac{A}{x-7}+\frac{B}{(x-7)^2}\]

  3. mathematics44
    • 2 years ago
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    Yeah, it was partial fractions. My bad. lol

  4. .Sam.
    • 2 years ago
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    So did you get it?

  5. mathematics44
    • 2 years ago
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    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?

  6. SithsAndGiggles
    • 2 years ago
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    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.

  7. mathematics44
    • 2 years ago
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    I tried 6 and 8 and answer that I got is A=10 , B= 1. I hope that's correct

  8. .Sam.
    • 2 years ago
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    \[x+3=B+A (x-7)\] When x=7 B=10 When B has this value, when x=0, 0+3=10-7A A=1 \[\frac{x+3}{(x-7)^2}=\frac{1}{x-7}+\frac{10}{(x-7)^2}\]

  9. .Sam.
    • 2 years ago
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    Can you do it now? \[\int\limits \left(\frac{10}{(x-7)^2}+\frac{1}{x-7}\right) \, dx\]

  10. mathematics44
    • 2 years ago
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    yes. thank you for your help

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