Chapter S1: Integrals

Ck2n sinh[2(n – k)x]

2(n – k) , n = 1, 2, . . .

10. ∫

cosh2n+1 x dx = 1 22n

Ck2n+1 sinh[(2n – 2k + 1)x]

2n – 2k + 1 = n∑ k=0

2k + 1 ,

n = 1, 2, . . .

11. ∫

coshp x dx = 1 p

sinh x coshp-1 x + p – 1 p

∫ coshp-2 x dx.