【摘要】 利用分部积分法和L′Hosp ita l法则得到了无穷积分∞∫0sin(βx)xncos(bx)dx(其中正整数n 1,实数β≠0,b 0)的一般计算公式,并且作为副产品得到了三个组合恒等式.更多还原

【Abstract】 In the article,some evaluations for the first kind of improper integrals ∫^∞₀sin（βx）xⁿcos（bx）dx for positive integer n1 and real numbers β≠0,b0 are established using the trigonometric power formulae, the L′Hospital rule,integration by part,and mathematical induction.As by-products,three combinatorial identities are obtained.更多还原