AP EAMCET · Maths · Indefinite Integration
\(\int e^{3 \log x}\left(x^4+1\right)^{-1} d x=\)
- A \(e^{3 \log x}+c\)
- B \(\frac{1}{4} \log \left(x^4+1\right)+c\)
- C \(\frac{1}{3} \log \left(x^4+1\right)+c\)
- D \(\frac{x^4}{x^4+1}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{4} \log \left(x^4+1\right)+c\)
Step-by-step Solution
Detailed explanation
\(I=\int e^{3 \log x}\left(x^4+1\right)^{-1} d x=\int x^3\left(x^4+1\right)^{-1} d x\) Let \(x^4+1=t \Rightarrow 4 x^3 d x=d t\) \[ \therefore \quad I=\frac{1}{4} \int \frac{d t}{t}=\frac{1}{4} \log _e(t)+C=\frac{1}{4} \log _e\left(x^4+1\right)+C \]
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