Question

How to integrate u^2/(sqrt(a^2-u^2)

Answer 1

is that supposed to be an a^2??

Answer 2

Yes, it is very similar to 1\[\frac{ 1 }{ a ^{2}+x ^{2} } = \frac{ 1 }{ a }\tan^{-1} \frac{ x }{ a }\] but is has the x^2 on top

Answer 3

It should be interesting this,
\[\int\frac{u^2}{\sqrt{a^2-u^2}}du=\int\frac{a^2}{\sqrt{a^2-u^2}}du-\int\frac{a^2-u^2}{\sqrt{a^2-u^2}}du\]
And I think it should be easy from this point.

Answer 4

How did you get you get that John_ES ?

Answer 5

are you doing trig substitution integrals yet?

Answer 6

yes

Answer 7

then they probably want you to use the substitution\[u=\frac1a\sec\theta\]

Answer 8

for the record, John ES used the fact that u^2=a^2-(a^2-u^2), but I don't think that is the way to go with this problem

Answer 9

Thx, will try that this afternoon