a) prove the convergency of $$ \int_0^{\infty} \dfrac {\cosh x \cdot \sin x} {x\cdot e^{x^2}}$$ b) prove the inequality $$ \int_0^{\frac {7\pi} {12}} \dfrac {\cosh x \cdot \sin x} {x\cdot e^{x^2}}<1$$ c) prove the inequality $$ \int_0^{\frac {2\pi} {3}} \dfrac {\cosh x \cdot \sin x} {x\cdot e^{x^2}}>1$$
I have used some Sandor aproximations for b)and c) and even some results of Zitian and Yebing but without success. Any kind of proof is welcome.Thanks!