求不定积分∫x[(1-x^4)]^(3⼀2)dx

2024-12-13 21:41:27
推荐回答(2个)
回答1:

先做换元u=x^2,1/2∫[(1-u^2)]^(3/2)du,然后再用三角换元

回答2:

∫xdx/√(1-x^4)^3
=(1/2)∫dx^2/√(1-x^4)^3
x^2=sinu
=(1/2)∫dsinu/cosu^3
=(1/2)∫du/cosu^2
=(1/2)tanu+C
=(1/2)x^2/√(1-x^4) +C