What is the value of \beta?
Consider the following for the next two (02) items that follow : Let \int\frac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{\frac{3}{2}}+\beta(x-1)^{\frac{3}{2}}+c
- A. -\frac{2}{3}
- B. -\frac{1}{3}
- C. \frac{1}{3} ✓
- D. \frac{2}{3}
Correct Answer: C. \frac{1}{3}
Explanation
Based on the rationalization and integration from the previous question, the result is \frac{1}{3}(x+1)^{3/2} + \frac{1}{3}(x-1)^{3/2} + c. Comparing the coefficient of (x-1)^{3/2}, we find \beta = \frac{1}{3}.
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