用部分积分法
∫(0,正无穷) x^2*3*e^(-3x)dx
=-[∫(0,正无穷) x^2*de^(-3x)]
=-[x2*e^(-3x)(0,正无穷）-∫(0,正无穷)e^(-3x)dx^2]
=-[0-∫(0,正无穷)e^(-3x)dx^2]
=∫(0,正无穷)e^(-3x)dx^2]
=∫(0,正无穷)2x*e^(-3x)dx]
=(-2/3)*∫(0,正无穷)xde^(-3x)]
=(-2/3)*[x*e^(-3x)(0,正无穷)-∫(0,正无穷)e^(-3x)dx]
=(-2/3)[0+(1/3)e^(-3x)(0,正无穷)]
=(-2/3)*(1/3)[0-1]
=2/9