Question:medium
If $\int \frac{5\sqrt{x}(4x^2 - 1)}{x} dx = 8\sqrt{x^5} + a\sqrt{x} + C$, where $a$ is a constant and $C$ is the constant of integration, then the value of $a$ is
If $\int \frac{5\sqrt{x}(4x^2 - 1)}{x} dx = 8\sqrt{x^5} + a\sqrt{x} + C$, where $a$ is a constant and $C$ is the constant of integration, then the value of $a$ is
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When the denominator is a single power of $x$, always split the fraction and use the power rule \( \int x^n dx = \frac{x^{n+1}}{n+1} \). It's simpler and less prone to error than substitution.
Updated On: Jun 24, 2026
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The Correct Option is C
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