求定积分∫（ x^3)[e^(-x^2)] dx 上限(ln2)^1/2,下限0

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∫x³e^(-x²) dx
=-1/2∫x²de^(-x²)
=-1/2x²e^(-x²)上限(ln2)^1/2,下限0+∫e^(-x²)xdx
=-1/2x²e^(-x²)上限(ln2)^1/2+∫e^(-x²)xdx
=-1/4ln2+∫e^(-x²)xdx
=-1/4ln2-1/2∫de^(-x²)
=-1/4ln2-1/2e^(-x²)上限(ln2)^1/2,下限0
=-1/4ln2+1/4
======以下答案可供参考======
供参考答案1:
先求原函数∫ (1/(1+x)+1/(2-x)) dx = ∫ 1/(1+x) dx + 原定积分= (ln 2 - ln 1) - (ln 1 - ln 2) = 0