Solving Integration Problems: Tips and Tricks for Integrating x arccos(x)dx

[colorado]

This is a problem from my homework set.

I'm so close but I'm tangled up at the end...

Integrate/ x arccos(x)dx

So far I am at

(x^2)/2 arccosx - Int/ (x^2)/ (2 sqrt(x^2 - 1))

Can figure out how to integrate this part.

 

[Dick]

I hope you mean sqrt(1-x^2). I would try a substitution like x=sin(u).

 

[colorado]

You are correct. Thankyou!

 

[Chrisas]

I'm not sure I'm reading this right. Is the part inside the integral,

x * arccos(x)?

if so, what about the substitution u = arccos(x), so that x=cos(u), and dx = -sin(u) du? Then it becomes the integral of -u*sin(u)*cos(u) du

I'd probably try repeated integration by parts to solve the new integral.

 

[Chrisas]

Never mind, seems it was answered while I was typing :)