Indefinite Integration
Integration by Substitution
Grade 12
Question:
<p>The value of $\displaystyle \int \frac{dx}{(1+x) \sqrt{x} \sqrt{1-x}}$ is equal to</p>
<p>(A) $\frac{1}{\sqrt{1-x}} + C$</p>
<p>(B) $\frac{2}{\sqrt{1-x}} + C$</p>
<p>(C) $\frac{1}{2\sqrt{1-x}} + C$</p>
<p>(D) none of these</p>
Step-by-Step Solution
Key Concept: Use appropriate substitution to simplify the product of square roots in the denominator
<p>This is an indefinite integral requiring substitution or algebraic manipulation.</p>
Correct Answer: B