Answer:
The answer is [tex]\frac{1}{30}\Big[2\log x-\log 6\Big][/tex]
Step-by-step explanation:
Given,
[tex]\int \frac{x^{5}-x^{4}}{5x^{6}-6x^5}dx[/tex]
[tex]=\int \frac{x^4(x-1)}{x^5(5x-6)}dx[/tex]
[tex]=\frac{1}{6}\int\Big[\frac{1}{x}+\frac{1}{5x-6}\Big]dx[/tex]
[tex]=\fracd{1}{6}\int \frac{1}{x}dx+\frac{1}{6\times 5}\int\frac{5}{5x-6}dx[/tex]
[tex]=\frac{1}{30}\Big[5\log x +\log (5x-6)\Big][/tex]
[tex]=\frac{1}{30}(2\log x-\log 6)[/tex]
Hence the result.
