Question

定积分 ∫上面9下面4 (根号X)/(根号X)-1 dx,先提前谢谢了~~在线等答案!!

Answer 1

(根号X)/(根号X-1) =(根号X -1 +1)/(根号X -1)=1+1/(根号X -1)
令t=根号X -1 x=(t+1)^2 dx=2(t+1)dt 1<=t<=2
∫上面9下面4 (根号X)/(根号X-1) dx
= ∫上面9下面4 (1+1/( (根号X-1 )dx
= ∫上面9下面4 dx+ ∫上面9下面4 (1/(根号X-1 )dx
=9-4+ ∫上面2下面1 (1/t*2(t+1)dt
=5+ ∫上面2下面1 (2+2/t)dt
=5+上面2下面 (2t+2lnt)
=5+2*2+2ln2-(2*1+2ln1)
=7+2ln2

Answer 2

qeddddddd

Answer 3

∫(4，9) √x/(√x-1) dx
令x=u²，dx=2u du
当x=4，u=2；x=9，u=3
= 2∫(2，3) u²/(u-1) du
= 2∫(2，3) [u + 1 + 1/(u-1)] du
= u² + 2u + 2ln|u-1|，(2，3)
= (9+6+2ln2) - (4+4)
= 7 + 2ln2