Indefinite Integrals

[jacks]

1. \(\displaystyle \int\frac{1}{\sin^5 x+\cos ^5 x}dx \)
2. If \(\displaystyle {I_n} = \int {\frac{1}{{\sin ^{2n + 1} x + \cos^{2n + 1}x}}dx}\). Then \(\displaystyle \mathop {\lim }\limits_{n \to + \infty } {I_n} = ?\)
   
   where \(n\in \mathbb{N}\)