let
dt/ √(1+t^4) = dF(t)
d/dx ∫ (x^2->x^3) dt/ √(1+t^4)
=d/dx [ F(x^3)-F(x^2) ]
=3x^2.F'(x^3) - 2xF'(x^2)
=3x^2/√(1+x^12) -2x/√(1+x^8)
求导,如题
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let
dt/ √(1+t^4) = dF(t)
d/dx ∫ (x^2->x^3) dt/ √(1+t^4)
=d/dx [ F(x^3)-F(x^2) ]
=3x^2.F'(x^3) - 2xF'(x^2)
=3x^2/√(1+x^12) -2x/√(1+x^8)