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?