请问这道不定积分题怎么做

Question

请问这道不定积分题怎么做如题如题如题如题如题如题

Answer 1

∫dx/√(x-a)(b-x)

=∫dx/√[-x^2+(a+b)x-ab]

=∫dx/√[-(x-(a+b)/2)^2+((a-b)/2)^2]

=∫d(x-(a+b)/2)/√[((a-b)/2)^2-(x-(a+b)/2)^2]

=arcsin[(x-(a+b)/2)/(a-b)/2]+C

=arcsin[(2x-(a+b))/(a-b)]+C1