Rewrite using trig identities =∫√(cos(x)+sin‌(x))2‌dx √(cos(x)+sin‌(x))2=((cos(x)+sin‌(x))), assuming ‌(cos(x)+sin‌(x))≥0 =∫cos(x)+sin‌(x)‌dx Apply the Sum Rule: ∫f(x)±g(x)‌dx=∫f(x)‌dx±∫g(x)‌dx =∫cos(x)‌dx+∫sin‌(x)‌dx ∫cos(x)‌dx=sin‌(x) ∫sin‌(x)‌dx=−cos(x) =sin‌(x)−cos(x) Add a constant to the solution =sin‌(x)−cos(x)+C