Question

how to integrate tan x

Answer 1

$I=\int {tan\ x} \, dx=\int {\frac{sin\ x}{cos\ x}} \, dx\\\\Let\ y=cos\ x,\ \ dy=-sin\ x\ dx\\\\I=\int\ {\frac{-dy}{y}} \, dy\\\\=-Ln\ |y| + K\\\\=Ln\ | secx|+ K$

Answer 2

-Ln(cosx) +k...... .