Question

求积分，这个定积分怎么积

Answer 1

。

追答

追问

没看懂

追答

哪里没看懂

哪一步

Answer 2

能

追问

咋积啊？

Answer 3

把x放到根号里面去再算

追问

放根号里咋算啊？？

Answer 4

令x=tant，dx=sec^2tdt
原式=∫(π/4,arctan2) sect/tant*sec^2tdt
=∫(π/4,arctan2) 1/sintcos^2tdt
=∫(π/4,arctan2) -d(cost)/sin^2tcos^2t
=∫(π/4,arctan2) d(cost)/(cost+1)(cost-1)cos^2t
=∫(π/4,arctan2) [-1/2(cost+1)+1/2(cost-1)-1/cos^2t]d(cost)
=[(-1/2)*ln(cost+1)+(1/2)*ln(1-cost)+1/cost]|(π/4,arctan2)
=[(1/2)*ln[(1-cost)/(1+cost)]+1/cost]|(π/4,arctan2)
=[lntan(t/2)+1/cost]|(π/4,arctan2)
=ln[(√5-1)/2]+√5-ln(√2-1)-√2
=ln[(√10+√5-√2-1)/2]+√5-√2