AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{\sqrt[4]{x}}{\sqrt{x}+\sqrt[4]{x}} d x=\frac{2}{3}\left[A \sqrt[4]{x^3}+B \sqrt[4]{x^2}+C \sqrt[4]{x}+D \log (1+\sqrt[4]{x})\right]+K\) then \(\frac{2}{3}(A+B+C+D)=\)
- A \(\frac{2}{3}\)
- B \(-\frac{2}{3}\)
- C \(\frac{4}{3}\)
- D \(-\frac{4}{3}\)
Answer & Solution
Correct Answer
(B) \(-\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{\sqrt[4]{x}}{\sqrt{x}+\sqrt[4]{x}} d x\) Let \(u=\sqrt[4]{x} \Rightarrow d u=\frac{1}{4 x^{3 / 4}} d x\) and \(\sqrt{x}=u^2 \Rightarrow x=u^4\)…
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