A community for students.
Here's the question you clicked on:
 0 viewing
Dido525
 3 years ago
Evaluate the Intergal
Dido525
 3 years ago
Evaluate the Intergal

This Question is Closed

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

Dido525
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1Not sure either, but what does \(x=\sin(u)\) get you?

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

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

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

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

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

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

BAdhi
 3 years 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
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0I would use integration by parts here right?

BAdhi
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0Now I need to figure out the integral of csc(x).
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.