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Dido525Best ResponseYou've already chosen the best response.0
\[\int\limits\limits_{}^{}\frac{ \arcsin(x) }{ x^2 } dx\]
 one year ago

Dido525Best 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

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

Dido525Best ResponseYou've already chosen the best response.0
Why would you do that?
 one year ago

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

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

Dido525Best 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

Dido525Best ResponseYou've already chosen the best response.0
What if I said u=arcsin(x) ?
 one year ago

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

Dido525Best 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

Dido525Best 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

Dido525Best ResponseYou've already chosen the best response.0
\[\frac{ \arcsin(x) }{ x }\int\limits_{}^{}\frac{ 1 }{ x \sqrt{1x^2} }dx\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I am kinda stuck at this point.
 one year ago

BAdhiBest 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

Dido525Best 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

Dido525Best ResponseYou've already chosen the best response.0
I would use integration by parts here right?
 one year ago

BAdhiBest 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

Dido525Best ResponseYou've already chosen the best response.0
Now I need to figure out the integral of csc(x).
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Thanks I got this :) .
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Thank you too wio :) .
 one year ago
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