#160; #160; #160; #160; #160; #8747;2x+3x 12dx= #8747;2x 2+2+3x 12dx= #8747;2x 1+5x 12dx=2 #8747;dxx 1+5 #8747;x 1 2 #160;dx=2 #160;ln ...

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Factorization

∫ 2 x+3 x-12 ...

Question

$\int \frac{2 x + 3}{{(x - 1)}^{2}} d x$

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Solution

$\int (\frac{2 x + 3}{{(x - 1)}^{2}}) d x = \int [\frac{2 x - 2 + 2 + 3}{{(x - 1)}^{2}}] d x = \int [\frac{2 (x - 1) + 5}{{(x - 1)}^{2}}] d x = 2 \int \frac{d x}{(x - 1)} + 5 \int {(x - 1)}^{- 2} d x = 2 \ln |x - 1| + 5 [\frac{{(x - 1)}^{- 2 + 1}}{- 2 + 1}] + C = 2 \ln |x - 1| - \frac{5}{x - 1} + C$

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p

q

\frac{6 q - p}{6}

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