Mathematics

# $\int { \cfrac { \left( { x }^{ 3 }+3 \right) \left( x-2\right) }{ \left( { x }^{ 2 }-4x+4 \right) } }dx$

##### SOLUTION
We have,
$I=\int { \cfrac { \left( { x }^{ 3 }+3 \right) \left( x-2\right) }{ \left( { x }^{ 2 }-4x+4 \right) } }dx$

$I=\int { \cfrac { \left( { x }^{ 3 }+3 \right) \left( x-2\right) }{ \left( x-2 \right)^2 } }dx$

$I=\int { \cfrac { \left( { x }^{ 3 }+3 \right) }{ \left( x-2 \right) } }dx$

$I=\int \left(x^2+2x+4+\cfrac{11}{x-2}\right)dx$

$I=\dfrac{x^3}{3}+2\dfrac{x^2}{2}+4x+11\ln (x-2)+C$

$I=\dfrac{x^3}{3}+x^2+4x+11\ln (x-2)+C$

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

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