Answer:
B. [tex] \frac{1}{2} sin2x + c[/tex]
Step-by-step explanation:
[tex] \int \frac{1 - { tan}^{2}x }{1 + { tan}^{2}x } dx \\ \\ = \int \frac{1 - \frac{ {sin}^{2}x }{ {cos}^{2}x } }{ {sec}^{2}x } dx\\ \\ = \int \frac{ {cos}^{2} x - {sin}^{2}x }{ {cos}^{2} x \times {sec}^{2} x }dx \\ \\ = \int \frac{cos \: 2x}{1} dx \\ \\ = \int {cos \: 2x}dx \\ \\ = \frac{1}{2} sin2x + c[/tex]
