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mpj4

  • one year ago

Calculus: How do you use trigonometric substitution on this?

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  1. mpj4
    • one year ago
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    \[\int\limits\!\frac{x^9+x^4}{(x^5-5)^{10}}dx\]

  2. rational
    • one year ago
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    i would substitute \(u = x^5-5\)

  3. mpj4
    • one year ago
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    Yes, I have split it to \[\int\limits\!\frac{x^4}{(x^5-5)^9}+\int\limits\!\frac{6x^4}{(x^5-5)^{10}}\]

  4. rational
    • one year ago
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    that looks nice but partial fractions is not really needed here

  5. mpj4
    • one year ago
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    forgot the dx there

  6. rational
    • one year ago
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    direct u substitution will do

  7. mpj4
    • one year ago
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    ah, I couldn't do a u sub on this. Care to lead the way?

  8. mpj4
    • one year ago
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    ah, and I didn't use partial fraction. Just manipulated it a bit. I think I can handle the rest actually. A medal for your efforts my friend

  9. rational
    • one year ago
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    \[\int\limits\!\frac{x^9+x^4}{(x^5-5)^{10}}dx = \int\limits\!\frac{x^4(x^5+1)}{(x^5-5)^{10}}dx\] substitute \(u=x^5-5 \implies \frac{du}{5} = x^4dx\), the integral becomes \[\frac{1}{5}\int\frac{u+6}{u^{10}}\,du\]

  10. mpj4
    • one year ago
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    question. how did x^5-1 become u+6?

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