JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let \(I(x)=\int \sqrt{\frac{x+7}{x}} d x\) and \(I(9)=12+7 \log _e 7\) If I \((1)=\alpha+7 \log _e(1+2 \sqrt{2})\), then \(\alpha^4\) is equal to \(..........\).
- A \(63\)
- B \(62\)
- C \(61\)
- D \(64\)
Answer & Solution
Correct Answer
(D) \(64\)
Step-by-step Solution
Detailed explanation
\(\int \sqrt{\frac{x+7}{x}} d x\) Put \(x = t ^2\) \(d x=2 tdt\) \(\int 2 \sqrt{ t ^2+7} d t=2 \int \sqrt{ t ^2+\sqrt{7}^2} d t\) \(I ( t )=2\left[\frac{ t }{2} \sqrt{ t ^2+7}+\frac{7}{2} \ln \left| t +\sqrt{ t ^2+7}\right|\right]+ C\)…
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