∫x3−14x3−xdx is k4x+log⁡|x|−m16log⁡|2x−1|−l16log⁡|2x+1|+C then k+m+l=

Solution:

$\begin{array}{l} \frac{x^{3} - 1}{4 x^{3} - x} = \frac{1}{4} + \frac{\frac{1}{4} x - 1}{x (2 x - 1) (2 x + 1)} \\ = \frac{1}{4} + \frac{1}{x} - \frac{7}{8} \frac{1}{2 x - 1} - \frac{9}{8} \frac{1}{2 x + 1} \\ \int \frac{x^{3} - 1}{4 x^{3} - x} d x = \frac{1}{4} x + \log | x | - \frac{7}{16} \log | 2 x - 1 | \\ - \frac{9}{16} \log | 2 x + 1 | + C \end{array}$

$\int \frac{x^{3} - 1}{4 x^{3} - x} d x$ is $\frac{k}{4} x + \log | x | - \frac{m}{16} \log | 2 x - 1 | - \frac{l}{16} \log | 2 x + 1 | + C t h e n k + m + l =$

Solution:

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