求不定积分∫√x/(x^3/4+1)dx等于多少?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/14 03:33:15
求不定积分∫√x/(x^3/4+1)dx等于多少?求不定积分∫√x/(x^3/4+1)dx等于多少?求不定积分∫√x/(x^3/4+1)dx等于多少?∫√xdx/(x^(3/4)+1)=(2/3)∫d

求不定积分∫√x/(x^3/4+1)dx等于多少?
求不定积分∫√x/(x^3/4+1)dx等于多少?

求不定积分∫√x/(x^3/4+1)dx等于多少?
∫√xdx/(x^(3/4)+1)
=(2/3)∫d(x^(3/2)/(x^(3/4)+1)
=(4/3)∫x^(3/4)d(x^(3/4))/(x^(3/4)+1)
=(4/3)∫d(x^(3/4)) -(4/3)∫d(x^(3/4))/(x^(3/4)+1)
=(4/3)x^(3/4)-(4/3)ln|x^(3/4)+1|+C