Mathematics

Integrate: $$\dfrac { 3 x ^ { 2 } } { x ^ { 6 } + 1 }$$


SOLUTION
$$I=\displaystyle \int \dfrac{3x^2}{x^6 + 1} dx $$    

$$x^3 = t$$

$$3x^2 dx = dt$$

$$I=\displaystyle \int \dfrac{3x^2}{t^2 + 1} \times \dfrac{dt}{3x^2} = \int \dfrac{dt}{t^2 + 1}$$

$$= \tan^{-1} (t) + c$$

$$= \tan^{-1} (x^3) + C$$
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Subjective Medium Published on 17th 09, 2020
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