(2+4u)⼀(2-7u-4u^2)的积分是多少?求过程。。

2025-02-23 19:06:50
推荐回答(4个)
回答1:

(2+4u)/(2-7u-4u^2)=(2+4u)/(2+u)(1-4u)=(4/3)/(2+u)-(4/9)/(1-4u)
∫(2+4u)/(2-7u-4u^2)du
=∫(-2/3)/(2+u)du+∫(4/3)/(1-4u)du
=(-2/3)ln|2+u|-(1/3)ln|1-4u|+C

回答2:

回答3:

2(2U+1)/(U-4)(2U+1)=2/(U-4)

回答4:

∫(2+4u)/(2-7u-4u^2)

=-∫(2+4u)/(u+2)(4u-1)
=-2/3∫(2/(4u-1)+1/(u+2))du
=-1/3ln│4u-1│-2/3ln│u+2│+C