求定积分 1、∫(1-2){[(Inx)^2]/(x^3)}dx 2、∫(0-1){x/[e^(5x)]}dx
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/04 22:55:22
求定积分 1、∫(1-2){[(Inx)^2]/(x^3)}dx 2、∫(0-1){x/[e^(5x)]}dx
用分部积分法
用分部积分法
1.∫ { [(Inx)^2]/(x^3) } dx = (-1/2) ∫ (Inx)^2 d x^(-2)
= (-1/2) [ (Inx)^2 * x^(-2) ] + ∫ 2Inx * x^(-3) dx
= (-1/2) [ (Inx)^2 * x^(-2) ] - ∫ Inx d x^(-2)
= (-1/2) [ (Inx)^2 * x^(-2) ] - lnx ^ x^(-2) + ∫ x^(-3) dx
= (-1/2) [ (Inx)^2 * x^(-2) ] - lnx ^ x^(-2) - (1/2) x^(-2) + C
原式 = (-1/8) (ln2)^2 - ln2 /4 - 1/8
2.∫ x * e^(-5x) dx = (-1/5) ∫ x d e^(-5x) = (-1/5) x * e^(-5x) + (1/5) ∫ e^(-5x) dx
= (-1/5) x * e^(-5x) + (1/25) e^(-5x) + C
原式 = (-4/25) e^(-5) - 1/25
再问: 1题的第二行那里不是减号吗
再答: 1. I = (-1/2) [ (Inx)^2 * x^(-2) - ∫ 2Inx * x^(-3) dx ] = (-1/2) (Inx)^2 * x^(-2) + ∫ Inx * x^(-3) dx 系数改正了 = (-1/2) (Inx)^2 * x^(-2) - (1/2) ∫ Inx d x^(-2) = (-1/2) (Inx)^2 * x^(-2) - (1/2) lnx ^ x^(-2) + (1/2) ∫ x^(-3) dx = (-1/2) (Inx)^2 * x^(-2) - (1/2)lnx ^ x^(-2) - (1/4) x^(-2) + C 原式 = (-1/8) (ln2)^2 - ln2 /8 - 1/16
= (-1/2) [ (Inx)^2 * x^(-2) ] + ∫ 2Inx * x^(-3) dx
= (-1/2) [ (Inx)^2 * x^(-2) ] - ∫ Inx d x^(-2)
= (-1/2) [ (Inx)^2 * x^(-2) ] - lnx ^ x^(-2) + ∫ x^(-3) dx
= (-1/2) [ (Inx)^2 * x^(-2) ] - lnx ^ x^(-2) - (1/2) x^(-2) + C
原式 = (-1/8) (ln2)^2 - ln2 /4 - 1/8
2.∫ x * e^(-5x) dx = (-1/5) ∫ x d e^(-5x) = (-1/5) x * e^(-5x) + (1/5) ∫ e^(-5x) dx
= (-1/5) x * e^(-5x) + (1/25) e^(-5x) + C
原式 = (-4/25) e^(-5) - 1/25
再问: 1题的第二行那里不是减号吗
再答: 1. I = (-1/2) [ (Inx)^2 * x^(-2) - ∫ 2Inx * x^(-3) dx ] = (-1/2) (Inx)^2 * x^(-2) + ∫ Inx * x^(-3) dx 系数改正了 = (-1/2) (Inx)^2 * x^(-2) - (1/2) ∫ Inx d x^(-2) = (-1/2) (Inx)^2 * x^(-2) - (1/2) lnx ^ x^(-2) + (1/2) ∫ x^(-3) dx = (-1/2) (Inx)^2 * x^(-2) - (1/2)lnx ^ x^(-2) - (1/4) x^(-2) + C 原式 = (-1/8) (ln2)^2 - ln2 /8 - 1/16
求定积分 1、∫(1-2){[(Inx)^2]/(x^3)}dx 2、∫(0-1){x/[e^(5x)]}dx
求定积分∫( x^3)[e^(-x^2)] dx 上限(ln2)^1/2,下限0
求定积分 ∫[0,2] e^x/(e^(2x)+1)dx
求定积分∫上2下1 e^x(1+e^x)^3dx
求不定积分∫(1-Inx)/(x-Inx)^2 dx
求不定积分 ∫ (1-Inx)/(x-Inx)^2 dx
定积分 [0,1]x*e^x^2 dx
求定积分∫【1,0】(4-x^2)dx
定积分∫1 0(x/(1+x^2))dx
定积分 ∫(2 0)√(x-1)/x dx
求定积分:∫(上标是2 ,下标是0)(e^x)/[(e^x-1)^(1/3)]dx=
求定积分 ∫(上线5,下线0) ( x^3/ x^2 +1) dx