∫cos(x-1)dx、∫x^3e^x^2dx怎么解

Question

∫ cos(x-1)dx、 ∫ x^3e^x^2dx怎么解

Answer 1

∫ 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