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

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

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

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

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

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

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

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

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

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

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

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

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

BAdhi
 one year ago
Best ResponseYou've already chosen the best response.2First 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

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

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

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

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

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

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