∫ ( ln | x |/ x √1+ ln | x |) dx equals -

Question

∫ ( ln | x |/ x √1+ ln | x |) dx equals - (A) (2/3) √1+ ln |x|( ln |x|-2)+c (B) (2/3) √1+ ln | x |( ln | x |+2)+ c (C) (1/3) √1+ ln |x|( ln | x |-2)+ c (D) 2 √1+ ln | x |(3 ln | x |-2)+ c

Tardigrade Admin · Accepted Answer

Correct answer is (a) (2/3) √1+ ln |x|( ln |x|-2)+c

Q. $\int \frac{l n ∣ x ∣}{x 1 + l n ∣ x ∣} d x$ equals -

$\frac{2}{3} 1 + ln ∣ x ∣ (ln ∣ x ∣ - 2) + c$

$\frac{2}{3} 1 + ln ∣ x ∣ (ln ∣ x ∣ + 2) + c$

$\frac{1}{3} 1 + ln ∣ x ∣ (ln ∣ x ∣ - 2) + c$

$2 1 + ln ∣ x ∣ (3 ln ∣ x ∣ - 2) + c$

Correct answer is (a) $\frac{2}{3} 1 + ln ∣ x ∣ (ln ∣ x ∣ - 2) + c$

Q. ∫x1+ln∣x∣​ln∣x∣​dx equals -

32​1+ln∣x∣​(ln∣x∣−2)+c

32​1+ln∣x∣​(ln∣x∣+2)+c

31​1+ln∣x∣​(ln∣x∣−2)+c

21+ln∣x∣​(3ln∣x∣−2)+c