CUET · MATHS · PYQ PAPER 2025
\(\int \frac{x^3-1}{x^2} d x\) is equal to
- A \(\frac{x^2}{2}+x+c\), where \(c\) is constant of integration
- B \(\frac{x^2}{2}-\frac{1}{x}+c\), where \(c\) is constant of integration
- C \(\frac{x^2}{2}-x+c\), where \(c\) is constant of integration
- D \(\frac{x^2}{2}+\frac{1}{x}+c\), where \(c\) is constant of integration
Answer & Solution
Correct Answer
(D) \(\frac{x^2}{2}+\frac{1}{x}+c\), where \(c\) is constant of integration
Step-by-step Solution
Detailed explanation
\(\int \left( \frac{x^3}{x^2} - \frac{1}{x^2} \right) dx\) \(\int \left( x - x^{-2} \right) dx\) \(\frac{x^{1+1}}{1+1} - \frac{x^{-2+1}}{-2+1} + c\) \(\frac{x^2}{2} - \frac{x^{-1}}{-1} + c\) \(\frac{x^2}{2} + \frac{1}{x} + c\)
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