求积分2x^3/x^2+1

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求积分2x^3/x^2+1
求积分2x^3/x^2+1

求积分2x^3/x^2+1
∫2x^3/x^2+1dx
=∫[2x(x^2+1)-2x]/(x^2+1)dx
=∫(2x-2x/(x^2+1)dx
=∫2xdx-∫2x/(x^2+1)dx
=x^2-∫1/(x^2+1)d(x^2+1)
=x^2-ln(x^2+1)+C

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∫2x^3/x^2+1dx
=∫[2x(x^2+1)-2x]/(x^2+1)dx
=∫(2x-2x/(x^2+1)dx
=∫2xdx-∫2x/(x^2+1)dx
=x^2-∫1/(x^2+1)d(x^2+1)
=x^2-ln(x^2+1)+C

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