Question

$\int \frac{2x+3}{3x+2}dx$=$\frac{A}{3}x+\frac{B}{3}ln(3x+2)+c$

Find value of B-A

Answer 1

Multiplying and dividing the equation with 3

$\frac{1}{3}\int \frac{3(2x+3)}{3x+2}dx=\frac{1}{3}\int \frac{6x+9}{3x+2}dx$

Taking 2 common from the numerator

$=\frac{2}{3}\int \frac{3x+\frac{9}{2}}{3x+2}dx$

$=\frac{2}{3}\int \frac{3x+2+\frac{5}{2}}{3x+2}dx$

$=\frac{2}{3}\int \frac{3x+2}{3x+2}dx+\frac{2}{3}\int \frac{\frac{5}{2}}{3x+2}dx$

$=\frac{2}{3}\int 1.dx+\frac{2}{3}\times \frac{5}{2}\int \frac{1}{3x+2}dx$

$=\frac{2}{3}x+\frac{5}{3}ln(3x+2)+c$