Question:medium

If $\int \frac{x^2}{\sqrt{1-x }}dx = p\sqrt{1-x} (3x^2 + 4x + 8) + c$ where $c$ is a constant of integration, then the value of $p$ is

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When evaluating integrals of the form $\int \frac{P(x)}{\sqrt{ax+b dx$, a common strategy is to use the substitution $u = ax+b$ (or $u^2 = ax+b$) to simplify the radical. Always ensure all terms are converted to the new variable before integration.
Updated On: Apr 28, 2026
  • $\frac{2}{15}$
  • $\frac{2}{15}$
  • $\frac{4}{15}$
  • $-\frac{2}{15}$
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The Correct Option is A

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