NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.2 Question 24

✅ Step-by-Step Solution

1. Work on each open interval where the original integrand is real and defined.
2. The numerator is half the derivative of the denominator.
3. An antiderivative is F(x)=\(\frac{\log{\left(\left|{4 \sin{\left(x \right)} + 6 \cos{\left(x \right)}}\right| \right)}}{2}\).
4. Differentiate this expression to check that F′(x)=\(\frac{- 3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}}{4 \sin{\left(x \right)} + 6 \cos{\left(x \right)}}\). Add an arbitrary constant C on each domain component.