Solving improper integral using infinite series, Dirichlet eta function and Riemann zeta function

[@cipherunity]

At 0:21 when x tends to 0 , t tends to - ꝏ. I wrote t tends to 0 which is not correct. Sorry for this mistake.

[@r2k314]

Integral necessary to solve Newton's "shell theorem" 0 to pi of [r - Rcos(theta)]sin theta/ [r^2 +R^2 - 2rRcos(theta)]^3/2 d(theta). substitution and integration by parts is one method.

[@cipherunity]

I shall look into it. Thanks

[@_Heb_]

t = 0 at 0:21 should be t -> -∞?

[@cipherunity]

That is correct. It is a mistake. Thanks for catching that.

[@slavinojunepri7648]

Sweet

[@cipherunity]

Good