COMEDK · Maths · 28. Indefinite Integration
The value of \(\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) is
- A \(3 \sqrt{x}+3(\sqrt[3]{x})-6 \sqrt[6]{x}+\log (\sqrt[6]{x}+1)+C\)
- B \(2 \sqrt{x}+6(\sqrt[6]{x})-6 \log (\sqrt[6]{x}+1)+C\)
- C \(2 \sqrt{x}-3(\sqrt[3]{x})+6 \sqrt[6]{x}-6 \log (\sqrt[6]{x}+1)+C\)
- D None of the above
Answer & Solution
Correct Answer
(C) \(2 \sqrt{x}-3(\sqrt[3]{x})+6 \sqrt[6]{x}-6 \log (\sqrt[6]{x}+1)+C\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Let} I=\int \frac{d x}{\sqrt{x}+\sqrt[3]{x}}\) Put \(x=t^{6} \Rightarrow d x=6 t^{5} d t\)…
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