# Table of Integrals - Forms Involving sinh ax and cosh ax

The integrals below involve sinh ax and cosh ax.

1) int sinh ax*cosh ax  dx = (sinh^2 ax)/(2a)

2) int  sinh px*cosh qx  dx = (cosh(p+q)x)/(2(p+q))+(cosh(p-q)x)/(2(p-q))

3) int  sinh^n ax*cosh ax  dx = (sinh^(n+1)ax)/((n+1)a)

**[If n=-1, see integral #1 in the table involving coth ax]

4) int  cosh^n ax*sinh ax  dx = (cosh^(n+1)ax)/((n+1)a)

**[If n=-1, see integral #1 in the table involving tanh ax]

5) int  sinh^2 ax*cosh^2 ax  dx = (sinh 4ax)/(32a)-x/8

6) int  1/(sinh ax*cosh ax)  dx = 1/a ln tanh ax

7) int  1/(sinh^2 ax*cosh ax)  dx = -1/a tan^-1 sinh ax-(\text{csch}\ ax)/a

8) int  1/(sinh ax*cosh^2ax)  dx = (\text{sech}\ ax)/a+1/a ln tanh((ax)/2)

9) int  1/(sinh^2 ax*cosh^2 ax)  dx = -(2 coth 2ax)/a

10) int  (sinh^2 ax)/(cosh ax)  dx = (sinh ax)/a-1/atan^-1 sinh ax

11) int  (cosh^2 ax)/(sinh ax)  dx = (cosh ax)/a+1/a ln tanh ((ax)/2)

12) int  1/(cosh ax (1+sinh ax))  dx = 1/(2a) ln ((1+ sinh ax)/(cosh ax))+1/a tan^-1 e^(ax)

13) int  1/(sinh ax(cosh ax+1))  dx = 1/(2a) ln tanh ((ax)/2)+1/(2a(cosh ax+1))

14) int  1/(sinh ax(cosh ax-1))  dx = -1/(2a) ln tanh ((ax)/2)-1/(2a(cosh ax-1))