question_answer

If \[f\left( \frac{3x-4}{3x+a} \right)=x+2,\] then \[\int{f(x)\,\,dx}\] is equal to ________.

A)  \[\frac{8}{3}\,\,\log |1-x|+\frac{x}{3}+C\]

B)  \[-\frac{8}{3}\,\,\log |1-x|+\frac{2}{3}x+C\]

C)  \[{{e}^{x+2}}\log \left| \frac{3x-4}{3x+4} \right|+C\]

D)  \[{{e}^{\frac{^{3x-4}}{3x+4}}}-\frac{{{x}^{2}}}{2}-2x+C\]

E)  None of these