求不定积分x立方乘e的负x平方,

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求不定积分x立方乘e的负x平方,

求不定积分x立方乘e的负x平方,
求不定积分x立方乘e的负x平方,

求不定积分x立方乘e的负x平方,
∫x^3e^(-x^2)dx
=-1/2∫x^2e^(-x^2)*(-2x)dx
=-1/2∫x^2e^(-x^2)d(-x^2)
=-1/2∫x^2de^(-x^2)
=-x^2e^(-x^2) /2+1/2∫e^(-x^2)*dx^2
=-x^2e^(-x^2) /2-1/2∫e^(-x^2)*d(-x^2)
=-x^2e^(-x^2) /2-e^(-x^2) /2 +C
=(-x^2+1)e^(-x^2) /2 +C

∫x^3e^(-x^2)dx
=(-1/2) ∫x^2de^(-x^2)
=(-1/2)x^2e^(-x^2)+(1/2) ∫e^(-x^2)dx^2
=(-1/2)x^2e^(-x^2)-(1/2) e^(-x^2)+C
=(-1/2)(x^2+1)e^(-x^2) +C