TS EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{x\left(x^4+1\right)}=\)
- A \(\frac{1}{4} \log \left(\frac{x^4+1}{x^4}\right)+C\)
- B \(\frac{1}{4} \log \left(\frac{x^4}{x^4+1}\right)+C\)
- C \(\frac{1}{4} \log \left(x^4+1\right)+C\)
- D \(\frac{1}{4} \log \left(\frac{x^4}{x^4+2}\right)+C\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{4} \log \left(\frac{x^4}{x^4+1}\right)+C\)
Step-by-step Solution
Detailed explanation
\text { } \begin{aligned} \int \frac{d x}{x\left(x^4+1\right)} & =\int \frac{x^4+1-x^4}{x\left(x^4+1\right)} d x \\ & =\int \frac{x^4+1}{x\left(x^4+1\right)} d x-\int \frac{x^4}{x\left(x^4+1\right)} d x \\ & =\int \frac{1}{x} d x-\int \frac{x^3}{x^4+1} d x \\ & =\log |x|-\int…
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