Mathematics

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

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

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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