Question:
Find the integral of \( \frac{(\sqrt{x+1})^2}{x\sqrt{x + 2x + \sqrt{x}}} \).
Find the integral of \( \frac{(\sqrt{x+1})^2}{x\sqrt{x + 2x + \sqrt{x}}} \).
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For complex integrals, simplify the expression first by combining like terms or using substitution methods.
Updated On: Sep 14, 2025
- \( \sqrt{x} + k \)
- \( \frac{1}{2} \sqrt{x} + k \)
- \( 2 \sqrt{x} + k \)
- \( 2x + k \)
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The Correct Option is C
Solution and Explanation
To integrate the given expression, we use standard integration techniques for rational and square-root functions. The result simplifies to:
\[
\int \frac{(\sqrt{x+1})^2}{x\sqrt{x + 2x + \sqrt{x}}} dx = 2 \sqrt{x} + k.
\]
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