AP EAMCET · Maths · Indefinite Integration
\(\int \frac{1}{x^5 \sqrt[5]{x^5+1}} d x=\)
- A \(\frac{4}{\sqrt[5]{x^5+1}}+c\)
- B \(4 x^4\left(x^5+1\right)^{\frac{4}{5}}+c\)
- C \(-\frac{\left(x^5+1\right)^{\frac{4}{5}}}{4 x^4}+c\)
- D \(-\frac{\left(x^5+1\right)^{\frac{4}{5}}}{4 x^5}+c\)
Answer & Solution
Correct Answer
(C) \(-\frac{\left(x^5+1\right)^{\frac{4}{5}}}{4 x^4}+c\)
Step-by-step Solution
Detailed explanation
Let, \(\mathrm{I}=\int \frac{1}{x^5 \sqrt[5]{x^5+1}} d x=\int \frac{1}{1^{\frac{1}{5}}} d x\) \(x^6\left(1+\frac{1}{x^5}\right)^{\overline{5}}\) Let \(1+\frac{1}{x^5}=t \Rightarrow \frac{1}{x^6} d x=-\frac{1}{5} d t\) Now,…
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