Mathematics

Evaluate:
$$\displaystyle\int { \frac { { x }^{ 4 }+4 }{ { x }^{ 2 }-2x+2 }  } dx$$


ANSWER

$$\dfrac{x^3}{3}+x^2+2x+C$$


SOLUTION
Given,

$$\int \dfrac{x^4+4}{x^2-2x+2}dx$$

as $$\left(x^2+2x+2\right)\left(x^2-2x+2\right) =x^4+4$$

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

$$=\int (x^2+2x+2)dx$$

$$=\int x^2dx+\int 2xdx+\int 2dx$$

$$=\dfrac{x^3}{3}+x^2+2x+C$$
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Single Correct Medium Published on 17th 09, 2020
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