integrate

[mano91]

can the function   1/ 2sqrt(x-x^2) be integrated with a substitution?
the answer is sin inverse sqrt(x)  but i dont know the substitution required to get here...

[Over9000]

Fuk hard one

=
                     =
                     =

Recall the chain rule

let
=

so =


so

[mano91]

yeh thats how i approached it. but my question is do we need to know how to do it on the exam say with the example, to integrate the derivative of tan inverse ( 1/x )  etc etc.

[Over9000]

yeh thats how i approached it. but my question is do we need to know how to do it on the exam say with the example, to integrate the derivative of tan inverse ( 1/x )  etc etc.

The integral of the derivative of tan inverse (1/x) = tan inverse (1/x)

[mano91]

yes i know that but in actual fact, im using it as an example.
such as integrate -1/  x sqrt( x^2 -1)

it ends up as sin inverse 1/x.
r we meant to know how to do these?

[TrueTears]

You need to know the integrals of expressions which give sin, tan, cos inverse.

[mano91]

meaning?
just regular ones like tan inverse x/3  etc etc?

[TrueTears]

Meaning check your essential book (or whatever one you're using) on expressions which lead to inverse trigonometric functions. You need to know all of those.