simple integration problem! work shown need help!

[johnq2k7]

integral of tanh(ln(x) dx:

work shown:
from table of integration of hyberbolic forms:

integral of tanh(u) du= ln cosh(u) +C


therefore i got (1/x)* ln (cosh(ln(x)) +C as my answer

why is this wrong?

please help

 

[galactus]

$\displaystyle \int tanh(ln(x))dx$

Rewrite as $\displaystyle \int \frac{x^{2}-1}{x^{2}+1}dx$

$\displaystyle \int\left(1-\frac{2}{1+x^{2}}\right)dx$

$\displaystyle =x-2\int\frac{1}{1+x^{2}}dx$

$\displaystyle x-2tan^{-1}(x)$