∫dt/(cos^2(t/2)) 请详解

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/16 07:30:17
∫dt/(cos^2(t/2))请详解∫dt/(cos^2(t/2))请详解∫dt/(cos^2(t/2))请详解换元x=t/2t=2xdt=2dx原式=∫sec^2(x)2dx=2∫sec^2(x)

∫dt/(cos^2(t/2)) 请详解
∫dt/(cos^2(t/2)) 请详解

∫dt/(cos^2(t/2)) 请详解
换元
x=t/2
t=2x
dt=2dx
原式=∫sec^2(x)2dx
=2∫sec^2(x)dx
=2tanx+C
=2tan(t/2)+C
楼上的系数错了

原式=1/2∫sec²(t/2)d(t/2)
=1/2*tan(t/2)+C