大一高数不定积分求解 大一高数不定积分
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=[x/(1+x^2)^(1/2)]e^(arctanx)-∫[e^(arctanx)*(1+x^2)/(1+x^2)^(3/2)]-[e^(arctanx)*x^2/(1+x^2)^(3/2)]dx =[x/(1+x^2)^(1/2)]e^(arctanx)-∫[1/(1+x^2)^(1/2)]d[e^(arctanx)]=[(x-1)/(1+x^2)^(1/2)]e^(arctanx)-∫[xe^(arctanx)/(1+x^2)^(3/2)]dx∴∫[xe^(arctanx)/(1+x^2)^(3/2)]dx=[(x-1)/2(1+x^2)^(1/2)]*e^(arctanx)+C.
要图还是，说给你听
绛旓細=1/2 arctan(sin²x)+c
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