If $f\left(\frac{3 x-4}{3 x+4}\right)=x+2$, then $\int f(x) d x$ is:

$e^{x+2} \log \left|\frac{3 x-4}{3 x+4}\right|+c$

$\frac{8}{3} \log |1-x|+\frac{x}{3}+c$

$e^{[(3 x-4)(3 x+4)]}-\frac{x^2}{2}-2 x+c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f\left(\frac{3 x-4}{3 x+4}\right)=x+2

, then

\int f(x) d x

is:

View answer and explanation

Correct option: B

-\frac{8}{3} \log |1-x|+\frac{2}{3} x+c

Option B is correct because the integral can be solved by substitution and partial fractions.

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