#160; #160; #160; #160; #160; #160; #8747;12 3x+13x 2dx= #8747;dx2 3x+ #8747;3x 2 12dx=ln #160;2 3x 3+3x 2 12+13 12+1+C=ln #160;2 3x 3+23 ...

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Algebra of Complex Numbers

∫ 12-3 x+13 x...

Question

$\int \frac{1}{2 - 3 x} + \frac{1}{\sqrt{3 x - 2}} d x$

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Solution

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

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