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Dido525 Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits\limits_{}^{}\frac{ \arcsin(x) }{ x^2 } dx\]
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
I have no idea... I am think about trig substitutions but I am not sure about this...
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
Not sure either, but what does \(x=\sin(u)\) get you?
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Why would you do that?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.0
I was thinking about trying integration by parts... have you tried that yet? :)
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
It would get rid of the arcsin.
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
It's just a guess
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Well I was going to make a substitution and then use intergration by parts but I am not sure...
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
What if I said u=arcsin(x) ?
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
That's the same as x = sin(u)
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Right. But if I said that I would get a squart root and I could use trigonometric substitution.
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Allright so I so far got... Use intragtion by parts: u=arcsinx) \[du=\frac{ 1 }{ \sqrt{1x^2} }\] dv=x^2 dx v=x^1
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ \arcsin(x) }{ x }\int\limits_{}^{}\frac{ 1 }{ x \sqrt{1x^2} }dx\]
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
I am kinda stuck at this point.
 one year ago

BAdhi Group TitleBest ResponseYou've already chosen the best response.2
First do the substitution $$x=\sin(u)\implies dx=\cos(u)du$$ then $$\int \frac{\arcsin{x}}{x^2}\;dx=\int \frac{u\cos(u)}{\sin^2(u)}\;du=\int u\csc(u)\cot(u)\;du$$ $$\int u\frac{d(\csc(u))}{du}du$$ do the integration by parts
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Hmm let me see...
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
@BAdhi So I got to this point \[\int\limits_{}^{}ucsc(u)\cot(u) du\]
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
I would use integration by parts here right?
 one year ago

BAdhi Group TitleBest ResponseYou've already chosen the best response.2
we know that $$\frac{d\csc(u)}{du}=\csc(u)\cot(u)$$ then, $$\begin{align*}\int u\csc(u)\cot(u)\,du&=\int u\frac{d\csc(u)}{du}\,du\\ &=u\csc(u)+\int \csc(u)\,du \end{align*}$$
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Yep I got that far.
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Now I need to figure out the integral of csc(x).
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Thanks I got this :) .
 one year ago

wio Group TitleBest ResponseYou've already chosen the best response.1
could use x = sin(u)
 one year ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.0
Thank you too wio :) .
 one year ago
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