CUET · MATHS · PYQ PAPER 2025
The value of \(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to (where \(C\) is an arbitrary constant) :
- A \(\frac{4}{15}\left(1-\frac{1}{x^3}\right)^{5 / 4}+C\)
- B \(\frac{4}{15}\left(1+\frac{1}{x^3}\right)^{5 / 4}+C\)
- C \(\frac{4}{15}\left(1-\frac{1}{x^3}\right)^{4 / 5}+C\)
- D \(\frac{4}{15}\left(1+\frac{1}{x^3}\right)^{4 / 5}+C\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{15}\left(1-\frac{1}{x^3}\right)^{5 / 4}+C\)
Step-by-step Solution
Detailed explanation
\(I = \int \frac{x(1-x^{-3})^{1/4}}{x^5} dx = \int (1-x^{-3})^{1/4} x^{-4} dx\) Let \(u = 1-x^{-3}\). \(du = 3x^{-4} dx \implies \frac{1}{3} du = x^{-4} dx\) \(I = \int u^{1/4} \frac{1}{3} du = \frac{1}{3} \frac{u^{5/4}}{5/4} + C\)…
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