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

Question

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

Sum

Solution

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

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Indefinite Integral Problems

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Q 3 Q 2 Q 4

Chapter 19: Indefinite Integrals - Exercise 19.03 [Page 23]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.03 | Q 3 | Page 23

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