Question

Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.

विकल्प

• `sec^2 (π/4 - x) + c`

• `-sec^2 (π/4 - x) + c`

• `log |sec(π/4 - x)| + c`

• `- log |sec(π/4 - x)| + c`

Answer 1

Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is `underlinebb(- log |sec(π/4 - x)| + c)`.

Explanation:

Let I = `int (tanx - 1)/(tanx + 1) dx`

= `- int (1 - tanx)/(1 + tanx)dx`

= `-int (tan  π/4 - tanx)/(1 + tan  π/4 tanx)dx`

= `-int tan(π/4 - x)dx`

= `-log |sec(π/4 - x)| + c`