Indefinite Integration
General
Grade 12
Question:
Find $\int \frac{2(1+x^2) + 3\sqrt{1-x^2}}{(1+x^2)\sqrt{1-x^2}} dx$
Step-by-Step Solution
Key Concept: General
$$\int \frac{2(1+x^2) + 3\sqrt{1-x^2}}{(1+x^2)\sqrt{1-x^2}} dx = \int \left( \frac{2}{\sqrt{1-x^2}} + \frac{3}{1+x^2} \right) dx = 2 \sin^{-1} x + 3 \tan^{-1} x + C$$
Correct Answer: A