Question

Calculate the convergence integration values
|cos x|/x^2 dx, from zero to infinity

Answer 1

do you recall the power series for cos x? that might make life simpler ... and it might not

Answer 2

\[cos x = 1+\frac{x^2}{2!}+\frac{x^4}{4!}+\frac{x^6}{6!}+...\]
\[\frac{cos x}{x^2} = x^{-2}+\frac{x^0}{2!}+\frac{x^2}{4!}+\frac{x^4}{6!}+\frac{x^6}{8!}...\]
integrating gives us
\[\int \frac{cos x}{x^2}dx = -x^{-1}+\frac{x^1}{2!}+\frac{x^3}{3~4!}+\frac{x^5}{5~6!}+\frac{x^7}{7~8!}...\]

at 0 its pointless; so the limit of this as x to inf, just make sure i didnt mess it up along the way ....