(%i1) f:sqrt((x-a)*(b-x))/x;
\[\tag{$f$}\label{f}\frac{\sqrt{\left( b-x\right) \,\left( x-a\right) }}{x}\]
(%i2) assume(a<b);
\[\tag{$\%{}o2$}\label{o2} [b < a]\]
(%i3) assume(a>0);
\[\tag{$\%{}o3$}\label{o3} [a > 0]\]
(%i4) integrate(f,x,a,b);
\[\tag{$\%{}o4$}\label{o4} -\left( -b-a\right) \,\operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2ab+{{a}^{2}}}}{b-a}\right) -2\sqrt{a}\,\sqrt{b}\,\operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2ab+{{a}^{2}}}}{b-a}\right) \]
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