计算定积分:∫1→2[x+(1/x)]^2dx
问题描述:
计算定积分:∫1→2[x+(1/x)]^2dx
答
13/3 + ln2。
答
∫[1,2][x+(1/x)]^2dx
=∫[1,2](x^2+1/x^2+2)dx
=(x^3/3-1/x+2x)[1,2]
=7/3+1/2+2
=29/6