Question

find the integral of x

Answer 1

$∫ \frac{cosx - sinx}{1 + 2 \sin(x) \cos(x) } \\ ∫ \frac{ \cos(x) - \sin(x) }{ {cos}^{2}x + {sin}^{2}x + 2 \sin(x) \cos(x) } \\ ∫ \frac{cosx - sinx}{ {(sinx \: + cosx)}^{2} } \\ take \:( sinx + cosx = t \\ cosx - sinx)dx = dt \\ \\ ∫ \frac{dt}{ {t}^{2} } \\ \frac{ - 1}{t} \\ \frac{ - 1}{ \sin(x) + \cos(x) }$