∫x*e^(-k^2*x^2)dx 扩号里是e的次方 从零到正无穷的定积分

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∫x*e^(-k^2*x^2)dx扩号里是e的次方从零到正无穷的定积分∫x*e^(-k^2*x^2)dx扩号里是e的次方从零到正无穷的定积分∫x*e^(-k^2*x^2)dx扩号里是e的次方从零到正无

∫x*e^(-k^2*x^2)dx 扩号里是e的次方 从零到正无穷的定积分
∫x*e^(-k^2*x^2)dx 扩号里是e的次方 从零到正无穷的定积分

∫x*e^(-k^2*x^2)dx 扩号里是e的次方 从零到正无穷的定积分
∫xe^(-k²x²) dx
= (1/2)∫e^(-k²x²) d(x²)
= (1/2)(1/-k²)∫e^(-k²x²) d(-k²x²)
= -1/(2k²)*e^(-k²x²)
= -1/(2k²)*[0-1/e^(0)]
= -1/(2k²)*(-1)
= 1/(2k²)

dawdaswd

∫xe^(-k²x²) dx 0到正无穷
= (1/2)∫e^(-k²x²) d(x²)
= (1/2)(1/-k²)∫e^(-k²x²) d(-k²x²)
= -1/(2k²)*e^(-k²x²)
= -1/(2k²)*(0-e^0)
= 1/(2k²)