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Table of Integrals - Forms Involving coshax

The integrals below involve coshax.

1)  coshax dx=sinhaxa

2)  xcoshax dx=xsinhaxa-coshaxa2

3)  x2coshax dx=-2xcoshaxa2+(x2a+2a3)sinhax

4)  coshaxx dx=lnx+(ax)222!+(ax)444!+(ax)666!+...

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+sinhaxcoshax2a

9)  xcosh2ax dx=x24+xsinh2ax4a-cosh2ax8a2

10)  1cosh2ax dx=tanhaxa

11)  coshaxcoshpx dx=sinh(a-p)x2(a-p)+sinh(a+p)x2(a+p)

12)  coshaxsinpx dx=asinhaxsinpx-pcoshaxcospxa2+p2

13)  coshaxcospx dx=asinhaxcospx+pcoshaxsinpxa2+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=2aq2-p2tan-1(qeax+pq2-p2)

                              OR =1ap2-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=12app2-q2ln(ptanhax+p2-q2ptanhax-p2-q2)

                                  OR =-1apq2-p2tan-1(ptanhaxq2-p2)

23) 1p2+q2cosh2ax dx=12app2+q2ln(ptanhax+p2+q2ptanhax-p2+q2)

                                 OR =1app2+q2tan-1(ptanhaxp2+q2)

24)  xmcoshax dx=xmsinhaxa-ma xm-1sinhax dx

                    **[See integral #18 in the table involving sinhax]

25)  coshnax dx=coshn-1axsinhaxan+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