Question

How do you integrate `(tan(x))/x`?

Answer 1

I don't believe there is an intrinsic function that is the anti-derivative

The power series solution is:
# int tanx/xdx = x+1/9x^3+2/75x^5-17/2205x^7+62/25515x^9+... #

Explanation:

I believe the only way to handle this integral is to use the Maclaurin power series for `tanx`; as follows;

`int tanx/xdx = int (x+1/3x^3+2/15x^5-17/315x^7+62/2835x^9+... )/xdx`

`:. int tanx/xdx = int 1+1/3x^2+2/15x^4-17/315x^6+62/2835x^8+...`

# :. int tanx/xdx = x+1/3x^3/3+2/15x^5/5-17/315x^7/7+62/2835x^9/9+... #

# :. int tanx/xdx = x+1/9x^3+2/75x^5-17/2205x^7+62/25515x^9+... #