What is U(x)V(x) equal to?
Direction: Consider the following for the two (02) items that follow : Let 2\int\frac{x^{2}-1}{\sqrt{x^{2}+1}}\,dx=U(x)V(x)-3\ln\{U(x)+V(x)\}+c
- A. \sqrt{x^{2}+x^{4}} ✓
- B. \sqrt{x+x^{3}}
- C. \frac{\sqrt{x^{2}+x^{4}}}{2}
- D. 2\sqrt{x^{2}+x^{4}}
Correct Answer: A. \sqrt{x^{2}+x^{4}}
Explanation
From the evaluation of the integral, we found U(x) = x and V(x) = \sqrt{x^2+1}. Multiplying them yields U(x)V(x) = x\sqrt{x^2+1} = \sqrt{x^2(x^2+1)} = \sqrt{x^4+x^2}.
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