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∫ 1 2 − 3 X + 1 √ 3 X − 2 D X - Mathematics

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प्रश्न

\[\int\frac{1}{2 - 3x} + \frac{1}{\sqrt{3x - 2}} dx\]
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उत्तर

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

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पाठ 19: Indefinite Integrals - Exercise 19.03 [पृष्ठ २३]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Exercise 19.03 | Q 3 | पृष्ठ २३

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