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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals2 Marks
Question
Integrate the function $\frac{3 x^{2}}{x^{6}+1}$
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Answer

Let $x^3 = t$
$\Rightarrow  3x^2 dx = dt$
$\Rightarrow \int \frac{3 x^{2}}{x^{6}+1} d x=\int \frac{d t}{t^{2}+1}$
$= \tan^{-1}t + C$
$= \tan^{-1}(x^3) + C$

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