∫cos(√x)dx 令√x=u,则dx/2√x=du,dx=2(√x)du=2udu, 原式=2∫ucosudu =2∫ud(sinu) =2[usinu-∫sinudu] =2(usinu+cosu)+C =2[(√x)sin(√x)+cos(√x)]+C ~~~~~~~~~~~~~~~~~~~~~~~~~ ∫√x(x+1)^2dx 令√x=t, 则dx=2tdt，带入 =∫t(t^2+1)^2*2tdt =∫2t^6+4t^4+2t^2dt =2/7t^7+4/5t^5+2/3t^3+c 反带回 =2/7(√x)^7+4/5(√x)^5+2/3(√x)^3+c ~~~~~~~~~~~~ ∫e^x/(1+e^x)^(1/2)dx =∫2d[(1+e^x)^(1/2)] =2(1+e^x)^(1/2)+c
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