Q71 / 160 · WBJEE 2011 · Mathematics

\(\int \frac{x^3 d x}{1+x^8}=\)

  • A
    \(4 \tan ^{-1} \mathrm{x}^3+\mathrm{c}\)
  • Correct answer
    B
    \(\frac{1}{4} \tan ^{-1} x^4+c\)
  • C
    \(x+4 \tan ^{-1} x^4+c\)
  • D
    \(x^2+\frac{1}{4} \tan ^{-1} x^4+c\)

Solution

Hints: \(\int \frac{x^3 d y}{1+\left(x^4\right)^2}=\frac{1}{4} \tan ^{-1}\left(x^4\right)\)

Hence, the correct answer is option: 'B'.

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