求不定积分∫√x/（x^3/4+1）dx等于多少?

1个回答

∫√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