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∫ 2 X − 1 ( X − 1 ) 2 D X - Mathematics

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Sum
\[\int\frac{2x - 1}{\left( x - 1 \right)^2} dx\]
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Solution

\[\int\left[ \frac{2x - 1}{\left( x - 1 \right)^2} \right]dx\]
\[ = \int\left[ \frac{2x - 2 + 2 - 1}{\left( x - 1 \right)^2} \right]dx\]
\[ = \int\left( \frac{2 \left( x - 1 \right)}{\left( x - 1 \right)^2} + \frac{1}{\left( x - 1 \right)^2} \right)dx\]
\[ = 2\int\frac{dx}{x - 1} + \int \left( x - 1 \right)^{- 2} dx\]
\[ = \text{2 ln }\left| x - 1 \right| + \frac{\left( x - 1 \right)^{- 2 + 1}}{- 2 + 1} + C\]
\[ = \text{2 ln }\left| x - 1 \right| - \frac{1}{x - 1} + C\]

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.4 | Q 6 | Page 30

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