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
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