Question Number 224100 by Jgrads last updated on 19/Aug/25
![Calculate I=∫^( +∞) _( 0) [(1/t)−(1/(sh(t)))]^( 2) dt](https://www.tinkutara.com/question/Q224100.png)
$$\mathrm{Calculate}\:\mathrm{I}=\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left[\frac{\mathrm{1}}{\mathrm{t}}−\frac{\mathrm{1}}{\mathrm{sh}\left(\mathrm{t}\right)}\right]^{\:\mathrm{2}} \mathrm{dt} \\ $$
Answered by MathematicalUser2357 last updated on 28/Aug/25
$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{{t}}−\frac{\mathrm{1}}{\mathrm{sinh}\:{t}}\right)^{\mathrm{2}} {dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$