TS EAMCET · Maths · Indefinite Integration
\(\int \frac{1}{x^m \sqrt[m]{x^m+1}} d x=\)
- A \(\frac{1}{m-1}\left(\frac{\sqrt[m]{x^m+1}}{x}\right)^m+c\)
- B \(\frac{-1}{m-1}\left(\frac{\sqrt[m]{x^m+1}}{x}\right)^{m-1}+c\)
- C \(\frac{-1}{m}\left(\frac{\sqrt[m]{x^m+1}}{x}\right)^m+c\)
- D \(\frac{1}{m}\left(\frac{\sqrt[m-1]{x^m+1}}{x}\right)^m+c\)
Answer & Solution
Correct Answer
(B) \(\frac{-1}{m-1}\left(\frac{\sqrt[m]{x^m+1}}{x}\right)^{m-1}+c\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \frac{1}{x^m\left(x^m+\right)^{\frac{1}{m}}} d x\) Let \(u=\mathrm{x}^{1-\mathrm{m}} ; d u=\frac{1-m}{x^m} d x\) \(x^m=u^{\frac{m}{1-m}}\)…
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