> 
> I am trying to solve this definite integral
>  $$3\int\_0^{\pi/2} \frac{\sqrt {\cos x}}{(\sqrt {\cos x}+\sqrt{\sin x})^5} \,dx$$
> 
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I take the following approach- I first remove the numerator by using the definite integral property

$$\int\_{a}^{b} f(x)dx=\int\_{a}^{b} f(a+b-x) dx$$
Using the above property and simplfying

$$\dfrac{3}{2}\int\_0^\frac{\pi}{2} \dfrac{sec^2x}{(1+\sqrt {tanx})^4} dx$$
Then I use the substitution $$\tan x=t$$
$$\Rightarrow \sec^2x dx=dt$$
Then I get a new integral 
$$\dfrac{3}{2}\int\_0^\infty \dfrac{dt}{(1+\sqrt t)^4}$$
I am stuck now because I do not know how to evaluate limits with infinity. Please help