The integrals below involve coshax.
1) ∫ coshax dx=sinhaxa
2) ∫ x⋅coshax dx=x⋅sinhaxa-coshaxa2
3) ∫ x2coshax dx=-2xcoshaxa2+(x2a+2a3)sinhax
4) ∫ coshaxx dx=lnx+(ax)22⋅2!+(ax)44⋅4!+(ax)66⋅6!+...
5) ∫ coshaxx2 dx=-coshaxx+a∫ sinhaxx dx
**[See integral #4 int the table involving sinhax]
6) ∫ 1coshax dx=2atan-1eax
7) ∫ xcoshax dx=1a2{(ax)22-(ax)48+5(ax)6144+...+(-1)nEn(ax)2n+2(2n+2)(2n)!+...}
8) ∫ cosh2ax dx=x2+sinhax⋅coshax2a
9) ∫ x⋅cosh2ax dx=x24+xsinh2ax4a-cosh2ax8a2
10) ∫ 1cosh2ax dx=tanhaxa
11) ∫ coshax⋅coshpx dx=sinh(a-p)x2(a-p)+sinh(a+p)x2(a+p)
12) ∫ coshax⋅sinpx dx=asinhax⋅sinpx-pcoshax⋅cospxa2+p2
13) ∫ coshax⋅cospx dx=asinhax⋅cospx+pcoshax⋅sinpxa2+p2
14) ∫ 1coshax+1 dx=1atanh(ax2)
15) ∫ 1coshax-1 dx=-1acoth(ax2)
16) ∫ xcoshax+1 dx=xatanh(ax2)-2a2lncosh(ax2)
17) ∫ xcoshax-1 dx=-xacoth(ax2)+2a2lnsinh(ax2)
18) ∫ 1(coshax+1)2 dx=12atanh(ax2)-16atanh3(ax2)
19) ∫ 1(coshax-1)2 dx=12acoth(ax2)-16acoth3(ax2)
20) ∫ 1p+qcoshax dx=2a√q2-p2tan-1(qeax+p√q2-p2)
OR =1a√p2-q2ln(qeax+p-√p2-q2qeax+p+√p2-q2)
21) ∫ 1(p+qcoshax)2 dx=qsinhaxa(q2-p2)(p+qcoshax)-pq2-p2∫ 1p+qcoshax dx
22) ∫ 1p2-q2cosh2ax dx=12ap√p2-q2ln(ptanhax+√p2-q2ptanhax-√p2-q2)
OR =-1ap√q2-p2tan-1(ptanhax√q2-p2)
23) ∫1p2+q2cosh2ax dx=12ap√p2+q2ln(ptanhax+√p2+q2ptanhax-√p2+q2)
OR =1ap√p2+q2tan-1(ptanhax√p2+q2)
24) ∫ xmcoshax dx=xmsinhaxa-ma∫ xm-1sinhax dx
**[See integral #18 in the table involving sinhax]
25) ∫ coshnax dx=coshn-1ax⋅sinhaxan+n-1n∫ coshn-2ax dx
26) ∫ coshaxxn dx=-coshax(n-1)xn-1+an-1∫ sinhaxxn-1 dx
**[See integral #20 in the table involving sinhax]
27) ∫ 1coshnax dx=sinhaxa(n-1)coshn-1ax+n-2n-1∫ 1coshn-2ax dx
28) ∫ xcoshnax dx=xsinhaxa(n-1)coshn-1ax+1(n-1)(n-2)a2coshn-2ax+n-2n-1∫ xcoshn-2ax dx