question_answer

\[\int{\sqrt{x+a\sqrt{ax-{{a}^{2}}}}dx,0<a<2}=\frac{2}{{{a}^{3/2}}}\] \[{{\{ax+a\sqrt{ax-{{a}^{2}}}\}}^{3/2}}-\frac{\sqrt{2}}{2}[A+B]+c\]Then

A)  \[A=\left[ \left\{ \left( \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2} \right)\sqrt{ax+{{a}^{2}}\sqrt{ax-{{a}^{2}}}} \right\} \right]\]

B)  \[B=\log \left[ \left\{ \left( \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2} \right)\sqrt{ax+a\sqrt{ax-{{a}^{2}}}} \right\} \right]\]

C)  \[A=\left\{ \left( \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2} \right)\sqrt{ax+a\sqrt{ax-{{a}^{2}}}} \right\}\]

D)  \[B=\log \left\{ \sqrt{ax-{{a}^{2}}}+\frac{{{a}^{2}}}{2}\sqrt{ax+a\sqrt{ax-{{a}^{2}}}} \right\}\]