Question 906055
<pre>
{{{int(dx/(sqrt(x)+x*sqrt(x)))}}}

{{{int(dx/( sqrt(x)(1+x) ))}}}

Let {{{u=sqrt(x)}}}, {{{u^2=x}}}
    {{{matrix(2,1,"",u=x^(1/2))}}}
    {{{matrix(2,1,"",du=expr(1/2)x^(-1/2)dx)}}}
    {{{du=dx/(2x^"1/2")}}}
    {{{du=dx/(2sqrt(x))}}}
    {{{du=dx/(2u)}}}
    {{{2u*du=dx}}}

Substitute for {{{x}}}, {{{dx}}}, and {{{sqrt(x)}}}

{{{int(2u*du/(u(1+u^2)))}}} 

{{{int(2cross(u)*du/(cross(u)(1+u^2)))}}}

{{{int(2du/(1+u^2))}}}

{{{2int(du/(1+u^2))}}}

{{{2*expr(1/1)arctan(u/1)+C}}}

{{{2arctan(u)+C}}}

{{{2arctan(sqrt(x))+C}}}

Edwin</pre>