Test for divergence of $\int_{0}^{\infty} \frac{\sin^2(x)}{x}dx$ without evaluating the integral I would like to prove that $$\int_{0}^{\infty} \frac{\sin^2(x)}{x}dx$$ diverges without actually evaluating the integral. Is there a convergence test from calculus or real analysis that can show that this integral diverges?
Thanks.
Edit: Someone pointed out that this is a possible duplicate. However, the question put forth as a possible duplicate asks about $\sin(x^2)$, not about $\sin^2(x)$.

Integrate from $x=n\pi$ to $x=(n+1)\pi$.  With the squared sine being nonnegative the integrand is greater than $(\sin^2x)/((n+1)\pi)$.  Conclude that the definite integral from $x=n\pi$ to $x=(n+1)\pi$ is greater than $\pi/(2(n+1))$ and then compare the full integral from $x=0$ to $x=\infty$ to the harmonic series.
