Question

$\int \frac{\ln | x |}{ x \sqrt{1+\ln | x |}} dx$ equals :

• A. $\frac{2}{3} \sqrt{1+\ln | x |}(\ln | x |-2)+ c$
• B. $\frac{2}{3} \sqrt{1+\ln | x |}(\ln | x |+2)+ c$
• C. $\frac{1}{3} \sqrt{1+\ln | x |}(\ln | x |-2)+ c$
• D. $2 \sqrt{1+\ln | x |}(3 \ln | x |-2)+ c$

Answer 1

Answer: (A)

$ \operatorname{Start} \ln | x |= t \Rightarrow \frac{1}{ x } dx = dt \Rightarrow \int \frac{ tdt }{\sqrt{1+ t }}$