sin(x/3)sin(nx)dx的不定积分
题目
sin(x/3)sin(nx)dx的不定积分
答案
积化和差公式:
sin(x/3)sin(nx) = (1/2)[cos(x/3 - nx) - cos(x/3 + nx)]
∫ sin(x/3)sin(nx) dx
= (1/2)∫ cos(x/3 - nx) dx - (1/2)∫ cos(x/3 + nx) dx
= (1/2)[1/(1/3 - n)]∫ cos[(1/3 - n)x] d[(1/3 + n)x] - (1/2)[1/(1/3 + n)]∫ cos[(1/3 + n)x] d[(1/3 + n)x]
= 1/[2(1/3 - n)]sin(x/3 - nx) - 1/[2(1/3 + n)]sin(x/3 + nx) + C
= [3/(2 - 3n)]sin(x/3 - nx) - [3/(2 + 3n)]sin(x/3 + nx) + C
举一反三
我想写一篇关于奥巴马的演讲的文章,写哪一篇好呢?为什么好
最新试题
热门考点