NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.3 Question 17

✅ Step-by-Step Solution

1. Work on each open interval where the original integrand is real and defined.
2. Split as sin x/cos²x+cos x/sin²x.
3. An antiderivative is F(x)=\(- \csc{\left(x \right)} + \sec{\left(x \right)}\).
4. Differentiate this expression to check that F′(x)=\(\frac{\sin^{3}{\left(x \right)} + \cos^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\). Add an arbitrary constant C on each domain component.