Question

不定积分题目？

大学高数不定积分
求手写详细过程，尽量不跳步

Answer 1

令y=x^4，则dy=4*x^3dx
原式
=1/4*∫dy/(1+y²)²
令y=tant，则dy=dt/cos²t
=1/4*∫cos²tdt
=1/8*∫(cos2t+1)dt
=1/16*sin2t+1/8*t+C
=1/8*y/(1+y²)+1/8*arctany+C
=1/8*x^4/(1+x^8)+1/8*arctanx^4+C
其中C为常数
注:
sin2t=2tant/(1+tan²t)

Answer 2

Answer 3

let
x= (sinu)^2
dx = 2sinu.cosu du
∫ arcsin√x/√(1-x) dx
=∫ (u/cosu)(2sinu.cosu du)
=2∫ u sinu du
=-2∫ u dcosu
=-2ucosu +2∫ cosu du
=-2ucosu +2sinu + C
=-2(arcsin√x) . √(1-x) + 2√x + C

追问

题目都没看啊