The integrals below involve `sinh ax`.
1) `int sinh ax dx = (cosh ax)/a`
2) `int x sinh ax dx = (x cosh ax)/a-(sinh ax)/a^2`
3) `int x^2 sinh ax dx = (x^2/a+2/a^3) cosh ax-(2x)/a^2 sinh ax`
4) `int (sinh ax)/x dx = ax+(ax)^3/(3*3!)+(ax)^5/(5*5!)+...`
5) `int (sinh ax)/x^2 dx = -(sinh ax)/x+aint (cosh ax)/x dx`
**[See integral #4 in the table involving `cosh ax`]
6) `int 1/(sinh ax) dx = 1/a ln tanh ((ax)/2)`
7) `int x/(sinh ax) dx = 1/a^2{ax-(ax)^3/18+(7(ax)^5)/1800-...+(2(-1)^n(2^(2n)-1)B_n(ax)^(2n+1))/((2n+1)!)+...}`
8) `int sinh^2 ax dx = (sinh ax cosh ax)/(2a)-x/2`
9) `int x*sinh^2 ax dx = (x sinh 2ax)/(4a)-(cosh 2ax)/(8a^2)-x^2/4`
10) `int 1/(sinh^2 ax) dx = -(coth ax)/a`
11) `int sinh ax*sinhpx dx = (sinh(a+p)x)/(2(a+p))-(sinh(a-p)x)/(2(a-p))`
**[For `a=+-p`, see integral #8 in this table]
12) `int sinh ax*sin px dx = (a cosh ax*sin px-p sinh ax *cos px)/(a^2+p^2)`
13) `int sinh ax*cos px dx = (a cosh ax*cos px+p sinh ax *sin px)/(a^2+p^2)`
14) `int 1/(p+q sinh ax) dx = 1/(asqrt(p^2+q^2))ln((qe^(ax)+p-sqrt(p^2+q^2))/(qe^(ax)+p+sqrt(p^2+q^2)))`
15) `int 1/(p+q sinh ax)^2 dx = (-q cosh ax)/(a(p^2+q^2)(p+q sinh ax))+p/(p^2+q^2) int 1/(p+q sinh ax) dx`
16) `int 1/(p^2+q^2 sinh^2 ax) dx = 1/(apsqrt(q^2-p^2)) tan^-1((sqrt(q^2-p^2)*tanh ax)/p)`
OR `= 1/(2apsqrt(p^2-q^2)) ln ((p+sqrt(p^2-q^2)*tanh ax)/(p-sqrt(p^2-q^2)*tanh ax))`
17) `int 1/(p^2-q^2 sinh^2 ax) dx = 1/(2apsqrt(p^2+q^2)) ln ((p+sqrt(p^2+q^2)*tanh ax)/(p-sqrt(p^2+q^2)*tanh ax))`
18) `int x^m sinh ax dx = (x^m cosh ax)/a-m/a int x^(m-1) cosh ax dx`
**[see integral #24 in the table involving `cosh ax`]
19) `int sinh^n ax dx = (sinh^(n-1) ax cosh ax)/(an)-(n-1)/n int sinh^(n-2) ax dx`
20) `int (sinh ax)/x^n dx = (-sinh ax)/((n-1)x^(n-1))+a/(n-1) int (cosh ax)/x^(n-1) dx`
**[see integral #26 int the table involving `cosh ax`]
21) `int 1/(sinh^n ax) dx = (-cosh ax)/(a(n-1)sinh^(n-1) ax)-(n-2)/(n-1) int 1/(sinh^(n-2) ax) dx`
22) `int x/(sinh^n ax) dx = (-x cosh ax)/(a(n-1)sinh^(n-1)ax)-1/(a^2(n-1)(n-2)sinh^(n-2)ax)-(n-2)/(n-1) int x/(sinh^(n-2) ax) dx`