用的是分部积分
-4∫[0→+∞] y²[e^(-4y)-e^(-2y)] dy
=-4∫[0→+∞] y²e^(-4y) dy + 4∫[0→+∞] y²e^(-2y) dy
=∫[0→+∞] y² de^(-4y) - 2∫[0→+∞] y² de^(-2y)
=y²e^(-4y) - 2∫[0→+∞] ye^(-4y) dy - 2y²e^(-2y) + 4∫[0→+∞] ye^(-2y)dy |[0→+∞]
=-2∫[0→+∞] ye^(-4y) dy + 4∫[0→+∞] ye^(-2y)dy
=(1/2)∫[0→+∞] y de^(-4y) - 2∫[0→+∞] yde^(-2y)
=(1/2)ye^(-4y) - (1/2)∫[0→+∞] e^(-4y) dy - 2ye^(-2y) + 2∫[0→+∞] e^(-2y)dy |[0→+∞]
=-(1/2)∫[0→+∞] e^(-4y) dy + 2∫[0→+∞] e^(-2y)dy
=(1/8)e^(-4y) - e^(-2y) |[0→+∞]
=-1/8 + 1
=7/8
希望可以帮到你,如果解决了问题,请点下面的"选为满意回答"按钮.