int_2^3 dx/(x(x^3 - 1)) = ______.

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`int_2^3 dx/(x(x^3 - 1)) = bbunderline((1)/(3) log ($\frac{208}{189}$)). Explanation: int_2^3 dx/(x(x^3 - 1))` x3 − 1 = y $\Rightarrow$ 3x2 dx = dy $\Rightarrow$ x^2 dx = dy/3 $\Rightarrow$ int_7^26 (dy/3)/((y + 10 y) $\Rightarrow$ $\frac{1}{3}$ int_7^26 dy/(y (y + 1)) 1/y - 1/(y + 1) $\Rightarrow$ (y + 1 - y)/(y(y + 1) $\Rightarrow$ `$\frac{1}{3}$ int_7^26(1/y - 1/(y + 1)) dy int1/(y + a) dy = log (y + a) $\Rightarrow$ 1-3 [log y - log (y + 1)]_7^26 $\Rightarrow$ $\frac{1}{3}$ {(log 26 - log 7) - (log 27 - log 8)} $\Rightarrow$ $\frac{1}{3}$ (log $\frac{26}{7}$ - log $\frac{27}{8}$) = $\frac{1}{3}$ log (26 xx 8)/(7 xx 27) $\Rightarrow$ I = $\frac{1}{3}$ log $\frac{208}{189}$`

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