MHT CET · Maths · Indefinite Integration
\(\int \frac{\mathrm{d} x}{\sqrt{x}+x}=\)
- A \(\log \sqrt{x}+c, \quad\) where \(c\) is the constant of integration.
- B \(\log (\sqrt{x}+x)+c, \quad\) where \(c\) is the constant of integration.
- C \(\log (1+\sqrt{x})+c, \quad\) where \(c\) is the constant of integration.
- D \(2 \log (1+\sqrt{x})+c, \quad\) where \(c\) is the constant of integration.
Answer & Solution
Correct Answer
(D) \(2 \log (1+\sqrt{x})+c, \quad\) where \(c\) is the constant of integration.
Step-by-step Solution
Detailed explanation
Let \(u = \sqrt{x}\), then \(\mathrm{d}x = 2u \, \mathrm{d}u\). \(\int \frac{2u \, \mathrm{d}u}{u+u^2}\)
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