AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{\log \left(1+x^4\right)}{x^3} d x=f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}(h(x))+c\), then \(h(x)\left[f(x)+f\left(\frac{1}{x}\right)\right]=\)
- A \(h(x) g(-x)\)
- B \(\frac{g(x)}{2}\)
- C \(g(x)+g(-x)\)
- D \(g(x) h(x)\)
Answer & Solution
Correct Answer
(B) \(\frac{g(x)}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } \int \frac{\log \left(1+x^4\right)}{x^3} d x \\ = & f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}(h(x))+c \\ \Rightarrow & \int x^{-3} \log \left(1+x^4\right) d x \\ = & \log \left(1+x^4\right) \cdot \frac{x^{-2}}{-2}+\frac{1}{2}…
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