Question

Evaluate: \(\int\frac{6}{x(2logx)^2 + 7logx + 5}dx\)

Answer 1

\(\int\frac{6}{x(2logx)^2 + 7logx + 5}dx\)

Let 6 = A(t + 1) + B(2t + 5) 

put t = -1, 6 = B(3) ⇒ B = 2

Equate the coefficient of t both sides 

0 = A + 2B 

A = -2B = -4

= – 2log(2log x + 5) + 2log(logx + 1) + C