How do you integrate $\int tan x$ $int tanx$ using substitution?

Question

4211 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-19T11:34:28

$\int tan x d x = - ln (cos x) + C$ $int tanx dx = -ln(cosx) + C$

$tan x = \frac{sin x}{cos x}$ $tanx = sinx/cosx$

$\int \frac{sin x}{cos x} d x$ $int sinx/cosx dx$

Let $u = cos x \Rightarrow d u = - sin x d x$ $u = cosx implies du = -sinxdx$

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

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

How do you integrate int tanx∫tanxint tanx using substitution?