一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算

Some Evaluations for the First Kind of Improper Integralintegral from n=0 to ∞(((sin(θ_x))/x)~ndx)

利用三角函数幂公式、L′Hospital法则、分部积分公式,得到含有三角函数的第一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算公式,其中n≥1且θ≠0.

Evaluations of the first kind of improper integrals ∫~∞_0sin(θx)x^ndx for positive integer n≥1 and θ≠0 are established using the trigonometric power formulae, the L′Hospital rule, integration by part, and mathematical induction.