Yikes. That was a latex typo, my apologies. Thank you for pointing out that dx error, i was under the impression that the 2xwould come from the derivative of x^{2}. I am learning this all from a set of notes and some videos, all by myself (no teacher or classmates) so it feels very overwhelming...
Homework Statement
This is the problem I was given:
I_{n} = \int^{0}_{\infty}(1 + x^{2})^{-n} dx
I was told to "deduce that"
I_{n} = 2n(I_{n} - I_{n + 1})
so I can "Hence or otherwise show that"
\int^{0}_{\infty}(1 + x^{2})^{-4} dx = \frac{5\pi}{32}
Homework Equations
I...