Math, asked by khushikdm31, 7 months ago

integrate 1 upon x(x-1) dx​

Answers

Answered by senboni123456
0

Step-by-step explanation:

We have,

  \int \frac{dx}{x(x - 1)}

 =   \int \frac{dx}{ {x}^{2} - x }

 =   \int \frac{dx}{ {x}^{2} - x +  { (\frac{1}{2}) }^{2}  - ( { \frac{1}{2} })^{2}   }

 =   \int \frac{dx}{(x -  \frac{1}{2} )^{2} -  ({  \frac{1}{2}  })^{2}  }

 =  \frac{1}{2 \times  \frac{1}{2} } ln  \: | \frac{(x -  \frac{1}{2}) -  \frac{1}{2}  }{(x -  \frac{1}{2} ) +  \frac{1}{2} } |  + c

 =  ln \: | \frac{x - 1}{x} | + c

 =  ln \:  |x - 1|   -  ln \:  |x|   + c

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