Question

\[\int \frac{dx}{\sinh x}\]
Options are:
a)cosh x +c
b)log\(\frac{e^x-1}{e^x+1}\)
c)\(\frac{\log e^{2x}}{1+e^x}+c\)
d)-cosh x +c

Answer 1

I missed +c in option b

Answer 2

Clearly, options (a) and (d) are out.
Integrating csch(x) gives ln(tanh(x/2)). Does that help?

Answer 3

\[\sinh x = \frac{e^{x}-e^{-x}}{2}\]Take e^x = t
e^x dx = dt, integral now converts to
\[\int\limits \frac{2}{t^{2}-1}dt\]

Can you take it off from here ? Its just simple partial fractions

Answer 4

so, its option b.
Thanks @FoolAroundMath

Answer 5

And thanks @QuantumModulus