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Question
Integrate the function `(3x^2)/(x^6 + 1)`
Solution
Let `I = int (3x^2)/(x^6 + 1) dx`
x3 = t Substituting,
3x2 dx = dt
Hence, `I = int 1/(t^2 + 1) dt ... (because d/dx tan^-1 x = 1/(1 + x^2))`
= tan-1 t + C
= tan-1 x3 + C
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