AP EAMCET · Maths · Indefinite Integration
If \(g\left(\frac{t+1}{2 t+1}\right)=t+1\), then \(\int g(x) d x=\)
- A \(\frac{x^2}{2}+c\)
- B \(\log _e(2 x-1)+\frac{1}{2} \log _e|(x+1)|+c\)
- C \(\frac{1}{2} \log _e\left|\left(\frac{x+1}{2 x+1}\right)\right|+c\)
- D \(\frac{x}{2}+\frac{1}{4} \log _e|2 x-1|+c\)
Answer & Solution
Correct Answer
(D) \(\frac{x}{2}+\frac{1}{4} \log _e|2 x-1|+c\)
Step-by-step Solution
Detailed explanation
\(g\left(\frac{t+1}{2 t+1}\right)=t+1\) replacing \(\frac{t+1}{2 t+1}\) by \(x\), we get,…
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