∫
xsinhax dx=^1 axcoshax−a^12 sinhax+C∫
x^2 sinhax dx=(
x^2
a +2
a^3)
coshax−^2 ax 2 sinhax+C∫
xnsinhax dx=^1 axncoshax−na∫
xn−^1 coshax dx∫ 1
xsinhax dx=ax+(ax)^3
3 ·3!+(ax)^5
4 ·5!+···+C∫ 1
x^2 sinhax dx=−1
xsinhax+a∫ 1
xcoshax dx∫ 1
xnsinhax dx=−sinhax
(n−1)xn−^1 +a
n− 1∫ 1
xn−^1 coshax dx∫ dx
sinhax=1
aln|tanhax
2 |+C∫ x dx
sinhax=1
a^2[
ax−(ax)3
18 +frac7(ax)(^5) 1800 +···+ (−1)n2(2^2 n−1)Bna^2 n+1x^2 n+1
(2n+ 1)! +···
]
+C
592.
∫
sinh^2 ax dx= 21 axsinh2ax−^12 x+C
593.
∫
sinhnax dx=na^1 sinhn−^1 axcoshax−n−n^1
∫
sinhn−^2 ax dx
594.
∫
xsinh^2 ax dx= 41 axsinh 2ax− 81 a 2 cosh 2ax−^14 x^2 +C
595.
∫ dx
sinh^2 ax
=−^1 acothax+C
596.
∫ dx
sinh^3 ax
=− 21 acschaxcothax− 21 aln|tanhax 2 |+C
597.
∫ x dx
sinh^2 ax
=−^1 axcothax+a^12 ln|sinhax|+C
598.
∫
sinhaxsinhbx dx=2(a^1 +b)sinh(a+b)x−2(a^1 −b)sinh(a−b)x+C
599.
∫
sinhaxsinbx dx=a (^2) +^1 b 2 [acoshaxsinbx−bsinhaxcosbx] +C
600.
∫
sinhaxcosbx dx=a (^2) +^1 b 2 [acoshaxcosbx+bsinhaxsinbx] +C
Appendix C