∫f(x)dx=x^2+C 则∫(x*f(1-x^2))dx=

2025-06-21 01:44:29
推荐回答(1个)
回答1:

是用第一类换元法

∫xf(1-x^2)dx=-1/2×∫f(1-x^2)×(1-x^2)'dx=-1/2×∫f(1-x^2)d(1-x^2),令t=1-x^2,则

∫xf(1-x^2)dx=-1/2×∫f(t)dt=-1/2×(t^2+C1)=-1/2×(1-x^2)^2+C
C=1/2×C1