Let us assume
I = \(\int\limits_{0}^{\pi/2}\cfrac{1}{1+\sqrt{tan\text x}}d\text x
\)...equation 1
We know that
\(tan\text x=\cfrac{sin\text x}{cos\text x}\)
Substituting the value in equation 1 we have,
By property, we know that
Thus in equation 2
Adding equation 2 and 3
Thus