求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx

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求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx作变量代换：令

求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx
求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx

求解∫1/【(2X^2+1)*(X^2+1)^(1/2)】dx
作变量代换：令x=tanα
得到积分为∫1/[(2X^2+1)*(X^2+1)^(1/2)]dx=∫1/[((2tanα)^2+1)*((tanα)^2+1)^(1/2)]d(tanα)=∫cosα/[(sinα)^2+1]dα=∫d(sinα)/[(sinα)^2+1]=arctan[sinα]+c
因为sinα=x*(x^2+1)^(1/2),故得到积分结果为arctan[x*(x^2+1)^(1/2)]+c

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