Integrating $\cosh^{-3}{x}$

34 Views Asked by At

Can someone solve the following please: $\int{\cosh^{-3}{x}}$?

1

There are 1 best solutions below

0
On BEST ANSWER

Hint. Write the differential as $$\cosh^{-4}x\cosh x\,\mathrm dx=\cosh^{-4}x\,\mathrm d(\sinh x)=\frac{\mathrm d(\sinh x)}{(1+\sinh^2x)^2},$$ and by making the obvious substitution, you have a rational function as integrand, which you can do by the usual route -- partial fractions et. al.