用换元法计算下列定积分1、∫0→4 (√x/√x+1)dx 2、∫(0→π/2) cos^4xsin xdx 1、2ln

1、∫0→4 (√x/√x+1)dx
√x=t dx=2tdt t:0到2
∫0→4 (√x/√x+1)dx = ∫0→2 (2t^2/(t+1)dt
= 2∫0→2 (t^2-1+1)/(t+1)dt
=2∫0→2 (t-1+1/(t+1))dt=2[t^2/2-t+ln(t+1)](0,2)
=2ln3
2、∫(0→π/2) cos^4xsin xdx
cosx=t -sinx=dx=dt
∫(0→π/2) cos^4xsin xdx
=-∫(1→0) t^4dt
=∫(0→1) t^4dt
=1/5