Question

求不定积分x^2/√(9-x^2) 不能查积分表

Answer 1

x=3sint dx=3costdt
∫(x²/[9-x²])dx
=∫((9sin²t)/3|cost|)3costdt
=±9∫sin²tdt
=±9∫[1-cos2t]/2 dt
=±(9/2)[t-(1/2)sin2t]+c
=±(9/2)[t-sintcost]+c
=±(9/2)[arcsin(x/3)-(x/3)√(9-x²)/3]+c

Answer 2

令x=3cost dx=-3sintdt
∫x^2dx/√(9-x^2)
=-27∫（cost）^2sintdt/√(9-9（cost）^2)
=-9∫（cost）^2sintdt/sint
=-9∫（cost）^2dt
=-9 ∫（（1+cos2t）/2）dt

剩余自己解决

Answer 3

简单x=3sint dx=3costdt
∫(x²/[9-x²])dx
=∫((9sin²t)/3|cost|)3costdt
=±9∫sin²tdt
=±9∫[1-cos2t]/2 dt
=±(9/2)[t-(1/2)sin2t]+c
=±(9/2)[t-sintcost]+c
=±(9/2)[arcsin(x/3)-(x/3)√(9-x²)/3]+c