Mathematics

# Evaluate $\int { \cfrac { 1 }{ (x-1){ x }^{ 2 } } } dx$

##### SOLUTION
$\int \dfrac{1}{(x-1)x^2}dx$

Splitting the above expression in to partial fractions, this can be written as

$\Rightarrow \int{(\dfrac{1}{x-1}-\dfrac{1}{x}-\dfrac{1}{x^2})}dx$

$\Rightarrow \int{\dfrac{1}{x-1}dx-\int \dfrac{1}{x}dx-\int \dfrac{1}{x^2}}dx$

$\Rightarrow \log(x-1)-\log x+\dfrac{1}{x}$

$\Rightarrow \log(\dfrac{x-1}{x})+\dfrac{1}{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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• A. $\displaystyle \frac { 2 }{ 5 } \ln { \left| x \right| } -\frac { 3 }{ 7 } \ln { \left| x-2 \right| } +\frac { 1 }{ 35 } \ln { \left| x+5 \right| } +c$
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• D. $\displaystyle -\frac { 2 }{ 5 } \ln { \left| x \right| } +\frac { 3 }{ 7 } \ln { \left| x-2 \right| } -\frac { 1 }{ 35 } \ln { \left| x+5 \right| } +c$