求积分∫x^4/(1+^2)dx

求积分∫x^4/(1+^2)dx
求积分∫x^4/(1+^2)dx

求积分∫x^4/(1+^2)dx
∫(x^4/1+x^2)dx
=∫(x^4+x²-x²-1+1）/（1+x^2)dx
=∫(x²-1)+1/(x²+1)dx
=x³/3-x+arctanx+c

答：
∫ (x^4)/(1+x^2) dx
=∫ [(x^2-1)(x^2+1)+1]/(1+x^2) dx
=∫ x^2-1+1/(1+x^2) dx
=(1/3)x^3-x+arctanx+C

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