Astroparticle Physics

A.1 Selected Formulae 383∫e x dx = e x ,exponential function∫x e ax dx = eax(ax − 1) ,a2 ∫dx1 + e ax = 1 a ln e ax1 + e ax ,∫sin x dx =−cos x,trigonometric functions∫cos x dx = sin x,∫tan x dx =−ln cos x,∫ln x dx = x ln x − x.natural logarithm3. Specific Integrals∫ π/20cos x sin x dx = 1 2 ,∫ ∞0∫ ∞0∫ ∞0∫ ∞0∫ 10e −ax2 dx = 1 2√ πa ,x dxe x − 1 = π 26 ,x dxe x + 1 = π 2sin axxtriginometricGaussianexponentials12 ,{ π2for a>0dx =sin ax/x− π ,2for a