how to integrate this question

1/sinx + cosx

i m stucked after seperating cos+sinx/2+2sin2x + cosx-sinx/2+2sin2x

1/(sinx + cosx) = 1/√2sin(π/4 + x) = cosec(π/4 + x)/√2 Integral of cosec x is log|cosecx - cotx| hence The answer is log|cosec( π/4 + x) - cot(π/4 + x)|/√2