NCERT Class 12 Maths · Chapter 7 Integrals · Miscellaneous Exercise Question 39

✅ Step-by-Step Solution

1. Work on each open interval where the original integrand is real and defined.
2. Factor cos 2x and cancel one factor sin x+cos x on the original domain. Integrate its logarithmic derivative.
3. An antiderivative is F(x)=\(\log{\left(\left|{\sin{\left(x \right)} + \cos{\left(x \right)}}\right| \right)}\).
4. Differentiate this expression to check that F′(x)=\(\frac{\cos{\left(2 x \right)}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}\). Add an arbitrary constant C on each domain component.