Mathematics

# Solve $\displaystyle\int \dfrac { \left( x ^ { 3 } + 8 \right) ( x - 1 ) } { x ^ { 2 } - 2 x + 4 }dx$

##### SOLUTION
$\int { \cfrac { \left( { x }^{ 3 }+8 \right) \left( x-1 \right) }{ { x }^{ 2 }-2x+4 } } dx=\int { \cfrac { (x+2)({ x }^{ 2 }-2x+4)(x-1) }{ ({ x }^{ 2 }-2x+4) } } dx$
$=\int { (x+2)(x-1) } dx=\int { ({ x }^{ 2 }-x+2x-2) } dx=\int { ({ x }^{ 2 }+x-2) } dx=\cfrac { { x }^{ 3 } }{ 3 } +\cfrac { { x }^{ 2 } }{ 2 } -2x+c$
where $c$ is a constant of integration

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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