Question

integration of 5x+2/3x-4​

Answer 1

Given:

5x+2/3x-4​

To find:

Integration of 5x+2/3x-4​

Solution:

From given, we have,

Integration of 5x+2/3x-4​ is as follows:

$\int \frac{5x+2}{3x-4}dx\\\\=\int \frac{5x}{3x-4}dx+\int \frac{2}{3x-4}dx\\\\=\frac{5}{9}\left(3x-4+4\ln \left|3x-4\right|\right)+\frac{2}{3}\ln \left|3x-4\right|\\\\=\frac{5}{3}x-\frac{20}{9}+\frac{26}{9}\ln \left|3x-4\right|+C$

Therefore, the integration of 5x+2/3x-4​ is 5/3x - 20/9 + 26/9 ln|3x-4| + C