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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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best_answer

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

 

Posted by

manish

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