Question

نشان دهید که: $$ \int _0^ \infty \frac{cos(2 \pi x^{2} )}{ cosh^{2} ( \pi x)} dx= \frac{1}{4} $$ And$$ \int_0^ \infty \prod _ {k=1} ^n \frac{ k^{2} }{ k^{2} + x^{2} }dx= \frac{ \pi }{2}. \frac{n}{2n-1} $$