INTEGRATION indefinite.(d-125)

\int \frac{dx}{ 1 + \sqrt{x} \sqrt{x}.\sqrt{1 + x}}

x = tan^ 2 \theta

dx = 2tan \theta sec ^ 2\theta d\theta

integral becomes

\int \frac{ 2 tan \theta sec ^ 2 \theta }{ 1 + \sqrt{tan ^ 2\theta } . \sqrt{tan ^ 2\theta .\sqrt{1 + tan ^ 2\theta }}}

2\int \frac{sec \theta d\theta }{ 1 + tan \theta }

2\int \frac{\frac{1}{cos \theta } d\theta }{ 1 + \frac{sin \theta }{cos \theta }}

2\int \frac{ d\theta }{sin \theta + cos \theta }

x=cos^{2}2\theta
can also help