Table of Integrals, Series, and Products, 8th Edition

$\begin{array}{ll}{\displaystyle {\int }_0^{\infty }\frac{x^{\mu }\text{d}x}{coshx+cost}=\frac{2\Gamma \left(\mu +1\right)}{sint}{\displaystyle \sum _{k=1}^{\infty }{\left(-1\right)}^{k-1}\frac{sinkt}{k^{\mu +1}}}}\hfill & \left[\mu >-1,0<t<\pi \right]\hfill \end{array}$

  BII (96)(14)a

8. 

${\displaystyle {\int }_0^u\frac{x\text{d}x}{cosh2x-cos2t}=\frac{1}{2}}cos\text{ec}\text{2}t\left[L\left(\theta +t\right)-L\left(\theta -t\right)-2L\left(t\right)\right]$

  LO III 402

$\left[\theta =\arctan \left(tanhu\cot t\right),t\ne n\pi \right]$

3.532

1.¹¹ 

${\displaystyle {\int }_0^{\infty }\frac{x^n\text{d}x}{acoshx+bsinhx}=\frac{2n!}{a+b}{\displaystyle \sum _{k=0}^{\infty }\frac{1}{{\left(2k+1\right)}^{n+1}}{\left(\frac{b-a}{b+a}\right)}^k}}$

  GW (352)(5)

$\left[a>0,b>0,n>-1\right]$

2. 

$\begin{array}{ll}{\displaystyle {\int }_0^u\frac{xcoshx\text{d}x}{cosh2x-cos2t}}\hfill & =\frac{1}{2}cos\text{ec}t\{L\left(\frac{\theta +t}{2}\right)-L\left(\frac{\theta -t}{2}\right)+L\left(\pi -\frac{\psi +t}{2}\right)\hfill \\ +L\left(\frac{\psi -t}{2}\right)-2L(\frac{t}{2}\hfill \end{array}$