Mathematics · 2019
JEE Main · 8 April 2019, Shift 2 · Q74
If ∫ (d x)/(x^3(1+x^6)^2 / 3)=x f(x)(1+x^6)^(1/3)+C where C is a constant of integration, then the function f(x) is equal to:
If
$$\int \frac{d x}{x^3\left(1+x^6\right)^{2 / 3}}=x f(x)\left(1+x^6\right)^{\frac{1}{3}}+C
$$
where $\displaystyle C$ is a constant of integration, then the function $\displaystyle f(x)$ is equal to:
Official answer
(3)
$\displaystyle -\frac{1}{2 x^3}$
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JEE Main 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.