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# Integrate the functions 3x ^2/ x ^ 6 + 1

Q1  Integrate the functions $\frac{3x^ 2 }{x^6 + 1 }$

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The given integral can be calculated as follows

Let $x^3 = t$
, therefore, $3x^2 dx =dt$

$\Rightarrow \int\frac{3x^2}{x^6+1}=\int \frac{dt}{t^2+1}$

$\\=\tan^{-1} t +C\\ =tan^{-1}(x^3)+C$

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