f(x):=1/(sqrt(cos(x))+sqrt(sin(x)))^4;

F(x):='integrate(1/(sqrt(cos(x))+sqrt(sin(x)))^4,x);

F(x):= (-5*sin(x)^2+4*sqrt(sin(x))*cos(x)^(3/2)
-6*sin(x)^(3/2)*sqrt(cos(x))+3*sin(x)*cos(x)+2)/
(3*(sqrt(cos(x))-sqrt(sin(x)))*(sqrt(sin(x))+sqrt(cos(x)))^3);

define(g(x), (radcan(trigsimp(factor(diff(F(x),x))))));

is(equal(f(x),g(x)));