Integrate the following w. r. t. x : (2 log x + 3)/(x(3 log x + 2)[(log x)^2 + 1])

Question

Integrate the following w. r. t. x :

\(\frac{2\,log\,x + 3}{x(3\,log\,x + 2)\left[(log\,x)^2 + 1\right]}\)

(2 log x + 3)/(x(3 log x + 2)[(log x)² + 1])

Answer 1

(2 log x + 3)/(x(3 log x + 2)[(log x)² + 1])

Put t = 0, we get

Comparing coefficients of t² on both the sides, we get