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∫ 2 X + 3 ( X − 1 ) 2 D X - Mathematics

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प्रश्न

\[\int\frac{2x + 3}{\left( x - 1 \right)^2} dx\]
बेरीज
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उत्तर

\[\int\left( \frac{2x + 3}{\left( x - 1 \right)^2} \right)dx\]
\[ = \int\left[ \frac{2x - 2 + 2 + 3}{\left( x - 1 \right)^2} \right]dx\]
\[ = \int\left[ \frac{2\left( x - 1 \right) + 5}{\left( x - 1 \right)^2} \right]dx\]
\[ = 2\int\frac{dx}{\left( x - 1 \right)} + 5\int \left( x - 1 \right)^{- 2} dx\]
\[ = \text{2   ln }\left| x - 1 \right| + 5\left[ \frac{\left( x - 1 \right)^{- 2 + 1}}{- 2 + 1} \right] + C\]
\[ = \text{2 ln }\left| x - 1 \right| - \frac{5}{x - 1} + C\]

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पाठ 19: Indefinite Integrals - Exercise 19.04 [पृष्ठ ३०]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Exercise 19.04 | Q 4 | पृष्ठ ३०

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