AP EAMCET · Maths · Indefinite Integration
If \(f(x)=\frac{x}{\left(1+n x^n\right)^{1 / n}}\) for \(n \geq 2\), then \(\int x^{n-2} f(x) d x=\)
- A \(\frac{1}{n(n-1)}\left(1+n x^n\right)^{1-\frac{1}{n}}+C\)
- B \(\frac{1}{(n-1)}\left(1+n x^n\right)^{1-\frac{1}{n}}+C\)
- C \(\frac{1}{n(n-1)}\left(1+n x^n\right)^{1+\frac{1}{n}}+C\)
- D \(\frac{1}{n+1}\left(1+n x^n\right)^{1+\frac{1}{n}}+C\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{n(n-1)}\left(1+n x^n\right)^{1-\frac{1}{n}}+C\)
Step-by-step Solution
Detailed explanation
\(\int x^{n-2} f(x) d x=\int \frac{x^{n-1}}{\left(1+n x^n\right)^{1 / n}} d x\) Let \(1+n x n=\mathrm{t} \Rightarrow x^{n-1} d x=\frac{1}{n^2} d t\)…
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