求微分,3题,
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求微分,3题,求微分,3题,求微分,3题,y=ln(x+y)两端对x求导得y''=(1+y'')/(x+y)y''=1/(x+y-1)∫1/(x^2-1)dx=1/2∫[1/(x-1)-1/(x+1)]dx
求微分,3题,
求微分,3题,
求微分,3题,
y=ln(x+y)
两端对x求导得
y'=(1+y')/(x+y)
y'=1/(x+y-1)
∫1/(x^2-1)dx
=1/2∫[1/(x-1)-1/(x+1)]dx
=1/2ln[(x-1)/(x+1)]+C
∫x^4/(x^2+1)dx
=∫(x^4-1+1)/(x^2+1)dx
=∫[(x^2-1)+1/(x^2+1)]dx
=1/3x^3-x+arctanx+C