(十四) 含有对数函数的积分

$$ 132. \, \int\!\!\ln x dx=x\ln x -x +C $$

$$ 133.\,\int\!\! \frac {dx}{x\ln x}= \ln \vert \ln x \vert +C $$

$$ 134. \,\int\!\! x^n\ln x dx=\frac{1}{n+1}x^{n+1}(\ln x - \frac{1}{n+1})+C $$

$$ 135. \,\int\!\! (\ln x)^n dx=x(\ln x)^n - n \int\!\!(\ln x)^{n-1} dx $$

$$ 136. \,\int\!\! x^m (\ln x)^n dx=\frac{1}{m+1}x^{m+1}(\ln x)^n - \frac {n}{m+1} \int\!\! x^m (\ln x) ^{n-1} dx $$

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