Question

Evaluate $\int \frac{cos2x+2si{n}^{2}x}{co{s}^{2}x}dx$

Answer 1

$\text{Let}I=\int \frac{cos2x+2si{n}^2}{co{s}^{2}x}dx=\int \frac{co{s}^{2}x+si{n}^{2}x+2si{n}^{2}x}{co{s}^{2}x}dx=\int \frac{co{s}^{2}x+si{n}^{2}x}{co{s}^{2}x}dx\Rightarrow I=\int se{c}^{2}xdx=tanx+c$