Question

不定积分化简，问下怎么从左边式子化到右边式子

不定积分化简，问下怎么从左边式子化到右边式子蟹蟹

Answer 1

把积分结果代回即可

Answer 2

∫y^3 .e^(y^2/2) dy
=∫y^2 .de^(y^2/2)
=y^2.e^(y^2/2) -2∫y.e^(y^2/2) dy
=y^2.e^(y^2/2) -2∫de^(y^2/2)
=y^2.e^(y^2/2) -2e^(y^2/2) +C1
--------
e^(-y^2/2). [∫-y^3 .e^(y^2/2) dy + C]
=e^(-y^2/2). [∫-y^3 .e^(y^2/2) dy + C]
=e^(-y^2/2). [ -y^2.e^(y^2/2) +2e^(y^2/2) + C]
=-y^2 + 2 + Ce^(-y^2/2)