Find the value of the improper integral I=∫0∞dxxa+x−aI = \int_0^{\infty} \frac{dx}{x^a + x^{-a}}I=∫0∞xa+x−adx for 0<a<10 < a < 10<a<1.
π2asin(π/(2a))\frac{\pi}{2a \sin(\pi/(2a))}2asin(π/(2a))π
π2asin(aπ/2)\frac{\pi}{2a \sin(a\pi/2)}2asin(aπ/2)π
πa\frac{\pi}{a}aπ
π2sin(π/2)\frac{\pi}{2 \sin(\pi/2)}2sin(π/2)π