Question

How do you integrate `int tanx` using substitution?

Answer 1

`int tanx dx = -ln(cosx) + C`

Explanation:

`tanx = sinx/cosx`

`int sinx/cosx dx`

Let `u = cosx implies du = -sinxdx`

`therefore -int (du)/u = -ln(u) + C`

`therefore int tanx dx = -ln(cosx) + C`