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mpj4
 one year ago
Calculus: How do you use trigonometric substitution on this?
mpj4
 one year ago
Calculus: How do you use trigonometric substitution on this?

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mpj4
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits\!\frac{x^9+x^4}{(x^55)^{10}}dx\]

rational
 one year ago
Best ResponseYou've already chosen the best response.1i would substitute \(u = x^55\)

mpj4
 one year ago
Best ResponseYou've already chosen the best response.1Yes, I have split it to \[\int\limits\!\frac{x^4}{(x^55)^9}+\int\limits\!\frac{6x^4}{(x^55)^{10}}\]

rational
 one year ago
Best ResponseYou've already chosen the best response.1that looks nice but partial fractions is not really needed here

rational
 one year ago
Best ResponseYou've already chosen the best response.1direct u substitution will do

mpj4
 one year ago
Best ResponseYou've already chosen the best response.1ah, I couldn't do a u sub on this. Care to lead the way?

mpj4
 one year ago
Best ResponseYou've already chosen the best response.1ah, 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
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits\!\frac{x^9+x^4}{(x^55)^{10}}dx = \int\limits\!\frac{x^4(x^5+1)}{(x^55)^{10}}dx\] substitute \(u=x^55 \implies \frac{du}{5} = x^4dx\), the integral becomes \[\frac{1}{5}\int\frac{u+6}{u^{10}}\,du\]

mpj4
 one year ago
Best ResponseYou've already chosen the best response.1question. how did x^51 become u+6?
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