Question Number 86558 by 71285 last updated on 29/Mar/20
$$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{n},\underset{\:\mathrm{0}} {\overset{\pi} {\int}}{e}^{\mathrm{cos}^{\mathrm{2}} {x}} \mathrm{cos}^{\mathrm{3}} \left(\mathrm{2}{n}+\mathrm{1}\right){x}\:{dx}= \\ $$