Question

What is the integral of f(x)=√(x)/√(1=x^2)?

Answer 1

√(1=x^2)
???

Answer 2

\[\int\limits_{}^{}\frac{\sqrt{x}}{\sqrt{1-x^2}}dx\]

@byuckert is this your question?

Answer 3

Yes yes yes. I apologize for the typo.

Answer 4

do you know trig substitution?

Answer 5

Actually, it is a plus, not a minus.

Answer 6

I know that it is somewhat in the form of sinh^-1(x), but I don't know what to do with the numerator.

Answer 7

again, do you know trig substitution? it kinda looks like a trig substitution problem

Answer 8

No, we have not covered that.

Answer 9

meh ok wolfram alpha integrator gives a weird answer
anyways trig substitution in a nutshell

\[1+\tan^2\theta=\sec^2\theta\]
\[\sin^2\theta+\cos^2\theta=1\]

you need to know those 2
basically if 1+x^2 ever appears as a denominator

make the substitution
\[x=\tan\theta\]
\[dx=\sec^2\theta d\theta\]

\[\int\limits_{}{} \frac{\sqrt{\tan \theta}}{\sqrt{1+\tan^2 \theta}}\sec^2\theta d\theta\]

ok this looks messy so im probably missing
but yes thats trig substitution

Answer 10

I tried Wolfram, as well, and all it did was confuse me more. Thank you very much for taking the time to do this. So from there how are you able to solve the integral?

Answer 11

not really,
\[\int\limits_{}{}\sqrt{\tan \theta}\sec \theta d\theta\]
is what you would get if you simplified it

integrate by parts?
it just looks horrible to integrate, and im hoping i made a mistake somewhere

Answer 12

Could you do another substitution here? u-sub or similar?

Answer 13

I tried a u-sub in every way that I found possible and, really, none seem to work.

Answer 14

@completeidiot, yeah I know we are definitely not supposed to be integrating by parts yet. I appreciate it though.

Answer 15

no closed form for this integral

Answer 16

I feel like you're right. Sometimes I question my teacher's awareness...