Indefinite Integration
Irrational Functions
Premium Question
Grade 12
Question:
$\int \frac{dx}{\sqrt{x} + \sqrt{x + 1}}$ equals:
(1) $\frac{2}{3} [(x + 1)^{3/2} - x^{3/2}] + C$
(2) $\frac{2}{3} [(x + 1)^{3/2} + x^{3/2}] + C$
(3) $\frac{1}{3} [(x + 1)^{3/2} - x^{3/2}] + C$
(4) $(x + 1)^{3/2} - x^{3/2} + C$
Step-by-Step Solution
Key Concept: Rationalise the denominator by multiplying numerator and denominator by $(\sqrt{x + 1} - \sqrt{x})$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)