how to integrate (-4)/ ((x^2 +2x+2)^2) ? thxxxx?
回答 (1)
2016-03-23 11:06 am
✔ 最佳答案
Solx^2+2x+2=(x+1)^2+1
Set x+1=Tanw
w=ArcTan(x+1)
SinwCosw=(x+1)/(x^2+2x+2)
x^2+2x+2=sec^2 w
dx=Sec^2 wdw
∫－4dx/(x^2+2x+2)^2
=∫－4Sec^2 w/sec^4 w
=∫－4Cos^2 wdw
=∫－2(1+Cos2w)dw
=－2∫dw－∫Cos2wd(2w)
=－2w+Sin(2w)+c
=－2ArcTan(x+1)+2(x+1)/(x^2+2x+2)+c
收錄日期: 2021-04-18 14:37:18
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