NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.5 Question 17

✅ Step-by-Step Solution

1. Work on each open interval where the original integrand is real and defined.
2. Put u=sin x. Decompose 1/[(1−u)(2−u)]=1/(1−u)−1/(2−u), then integrate.
3. An antiderivative is F(x)=\(\log{\left(\left|{\frac{\sin{\left(x \right)} - 2}{\sin{\left(x \right)} - 1}}\right| \right)}\).
4. Differentiate this expression to check that F′(x)=\(\frac{\cos{\left(x \right)}}{\left(1 - \sin{\left(x \right)}\right) \left(2 - \sin{\left(x \right)}\right)}\). Add an arbitrary constant C on each domain component.