If $$a$$ is a real number such that $$\int_\limits0^a x d x \leq a+4$$ then

$$ \text { If } I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n x d x \text {, for } n \geq 2 \text {, then } I_n+I_{n-2}= $$

$$ \int_\limits0^{\frac{\pi}{2}} \frac{\cos x}{1+\cos x+\sin x} d x= $$

$$ \int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sqrt{\cos x-\cos ^3 x} d x \text { is equal to } $$