(126) Z e ax sinh bx dx =      e ax a 2 - b 2 [-b cosh bx + a sinh bx] a 6= b e 2 ax 4 a - x 2 a = b (127) Z tanh ax dx = 1 a ln cosh ax (128) Z e ax tanh bx dx =              e (a+2 b)x (a +2 b) 2 F 1 h 1+ a 2 b , 1, 2+ a 2 b , -e 2 bx i - 1 a e ax 2 F 1 h 1, a 2 b , 1+ a 2 b , -e 2 bx i a 6= b e ax - 2 tan -1 [e ax ] a a = b (129) Z cos ax cosh bx dx = 1 a 2 + b 2 [a sin ax cosh bx + b cos ax sinh bx] (130) Z cos ax sinh bx dx = 1 a 2 + b 2 [b cos ax cosh bx + a sin ax sinh bx] (131) Z sin ax cosh bx dx = 1 a 2 + b 2 [-a cos ax cosh bx + b sin ax sinh bx] (132) Z sin ax sinh bx dx = 1 a 2 + b 2 [b cosh bx sin ax - a cos ax sinh bx] (133) Z sinh ax cosh axdx = 1 4 a [-2 ax + sinh 2 ax] (134) Z sinh ax cosh bx dx = 1 b 2 - a 2 [b cosh bx sinh ax - a cosh ax sinh bx] c  2014. From http://integral-table.com, last revised June 14, 2014. This mate- rial is provided as is without warranty or representation about the accuracy, correctness or suitability of this material for any purpose. This work is licensed under the Creative Com- mons Attribution-Noncommercial-Share Alike 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. 14