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anonymous

  • 4 years ago

What is my inner-function g if I integrate x/(2-x)^3 with the method of substitution?

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  1. EscherichiaRinku
    • 4 years ago
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    If you think of powers as a function, then you will easily see that (2-x) is a function inside the power function. So, your g is g(x) = 2-x.

  2. anonymous
    • 4 years ago
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    that was simpler than it looked :S

  3. anonymous
    • 4 years ago
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    Escher, if you actually did that by integration, what would it look like?

  4. anonymous
    • 4 years ago
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    then of course you have to write \[u=2-x, du = -dx\] \[x=2-u\] and integrate \[-\int \frac{2-u}{u^3}du\]

  5. anonymous
    • 4 years ago
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    or if you prefer \[\int \frac{u-2}{u^3}du\]

  6. EscherichiaRinku
    • 4 years ago
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    And then substitute (2-x) back to get a result with the original terms :)

  7. EscherichiaRinku
    • 4 years ago
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    ^I mean, substitute (2-x) back after integration :D

  8. anonymous
    • 4 years ago
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    Oh, I did not know that I´m also able to replace the x upstairs (which annoyed) with 2-u. Thank you very much.

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