学帮网求微分,3题,
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/05 23:41:38
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
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来源：学生作业学帮网 编辑：学帮网 时间：2024/05/05 23:41:38
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