Mathematics

Integrate:
$$\int \dfrac { x ^ { 4 } } { x ^ { 2 } + 1 }$$ dx =


ANSWER

$$\dfrac { x ^ { 3 } } { 3 } - x + \tan ^ { - 1 } x + c$$


SOLUTION
$$\int \dfrac{x^{4}}{x^{2}+1}dx=\int \dfrac{x^{4}+1-1}{x^{2}+1}dx=\int (\dfrac{x^{4}-1}{x^{2}+1}+\dfrac{1}{x^{2}+1})dx$$

$$=\int ((x^{2}-1)+\dfrac{1}{x^{2}+1})dx$$

$$= \dfrac{x^{3}}{3}-x+tan^{-1}x+c$$
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Single Correct Medium Published on 17th 09, 2020
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