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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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2.47 Combinations of hyperbolic functions and powers

2.471

1.12 

xr sinhp x coshq x dx=1(p + q)2[ (p + q)xr sinhp+1 x coshq-1 xrxr1sinhp x coshq x + r(r + 1)xr2sinhp x coshq x dx+rpxr1sinhp1 x coshq1x dx + (q  1)(p + q)xr sinhp x coshq2 x dx]=1(p + q)2[ (p + q)xr sinhp1 x coshq+1 xrxr1sinhp x coshq x + r(r  1)xr2sinhp x coshq x dxrpxr1sinhp1 x coshq1x dx  (p  1)(p + q)xr sinhp2 x coshq x dx]

si1081_e

GU (353)(1)

2. 

xn sinh2m x dx=(1)m( m2m)xn+122m(n+1)+122m1k=0m1(1)k( k2m)xn cosh(2m2k)x dx

si1082_e

3. 

xn sinh2m+1 x dx

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