It would help if you wrote out
So your integral will now be:
If you let
you will find that
And then go from there...
Hey, was wondering if anyone could help out with a pointer on how to do this in a more structured fashion.
So the original task is to solve the indefinite integral of
sqrt(1-x^{2})/x^{4}
So taking a cue from the square root i substitute
x = sin(t)
dx = cos(t)dt
and get the integral of
cos^{2}(t)/sin^{4}(t)
And here my brain is going tilt, because I can't seem to figure out method will actually take me forward from there. What I did was working backwards, just playing around with trigonometric identities and finding that the derivative of
-1/3tan^{3}(t)
gives the integrand. Back substituting, using that
tan(t) = sqrt(1-x^{2})
confirms that this is the correct answer.
But yea, this isn't a very elegant way of doing it, so maybe someone could point out what I'm missing?
It would help if you wrote out
So your integral will now be:
If you let
you will find that
And then go from there...