mpj4
  • mpj4
Calculus: How do you use trigonometric substitution on this?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mpj4
  • mpj4
\[\int\limits\!\frac{x^9+x^4}{(x^5-5)^{10}}dx\]
rational
  • rational
i would substitute \(u = x^5-5\)
mpj4
  • mpj4
Yes, I have split it to \[\int\limits\!\frac{x^4}{(x^5-5)^9}+\int\limits\!\frac{6x^4}{(x^5-5)^{10}}\]

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rational
  • rational
that looks nice but partial fractions is not really needed here
mpj4
  • mpj4
forgot the dx there
rational
  • rational
direct u substitution will do
mpj4
  • mpj4
ah, I couldn't do a u sub on this. Care to lead the way?
mpj4
  • mpj4
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
rational
  • rational
\[\int\limits\!\frac{x^9+x^4}{(x^5-5)^{10}}dx = \int\limits\!\frac{x^4(x^5+1)}{(x^5-5)^{10}}dx\] substitute \(u=x^5-5 \implies \frac{du}{5} = x^4dx\), the integral becomes \[\frac{1}{5}\int\frac{u+6}{u^{10}}\,du\]
mpj4
  • mpj4
question. how did x^5-1 become u+6?

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