∫ cos(x-1)dx、 ∫ x^3e^x^2dx怎么解

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/05/01 04:59:59

∫ cos(x - 1) dx
= ∫ cos(x - 1) d(x - 1)
= sin(x - 1) + C
∫ x³e^(x²) dx
-->令u = x²,du = 2x dx-->
= ∫ uxe^u · du/(2x)
= (1/2)∫ ue^u du = (1/2)∫ u de^u
= (1/2)ue^u - (1/2)∫ e^u du
= (1/2)ue^u - (1/2)e^u + C
= (1/2)(u - 1)e^u + C
= (1/2)(x² - 1)e^(x²) + C

求不定积分∫e^2x * cos e^x dx ∫X^2 e^-X^3 dx. ∫e^x (1/X + ln×)dx 怎么解 ∫1/(1+cos^2(x)) dx ∫(1-cos^(2)2x)dx ∫cos((x/3)-1)dx=? ∫(1+sinx) / cos^2 x dx ∫ (1+cos^2 x)/cos^2 x dx = ∫e^(1\x)dx怎么算不定积分 ∫ x*cos(x/3)*dx ∫x／[(cos^2)x]dx ∫sin(x) cos^2(x)dx