[" 67."2[(1)/(2x+1)+(1)/(3(2x+1)^(3))+(1)/(5(2x+1)^(5))+...]" is eq "],[[" to "],[[" (1) "log((x)/(x+1))," (2) "log((x+1)/(x))],[" (3) "log(2x+1)," (4) "log((1)/(2x+1))]]]

log_(2)(x+1)-log_(2)(3x-1)=2

log x-(1)/(2)log(x-(1)/(2))=log(x+(1)/(2))-(1)/(2)log(x+(1)/(8))

[The value of "int(sqrt(x^(2)+1){log_(e) (x^(2)+1)-2log_(e)x})/(x^(4))dx" is equal to "],[" (a) "(2)/(3)(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))-(2)/(3)}+C],[" (b) "-(1)/(3)(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))-(2)/(3)}+C],[" (c) "(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))+(2)/(3)}+C ]

int(log(x+1)-log x)/(x(x+1))dx= (A) log(x-1)log x+(1)/(2)(log x-1)^(2)-(1)/(2)(log x)^(2)+c (B) (1)/(2)(log(x+1))^(2)+(1)/(2)(log x)^(2)-log(x+1)log x+c (C) -(1)/(2)(log(x+1)^(2))-(1)/(2)(log x)^(2)+log x*log(x+1)+c (D) [log(1+(1)/(x))]^(2)+c

log4+(1+(1)/(2x))log3=log(3^((1)/(x))+27)

If log_(x+1)(2x-1)+log_(2x-1)(x+1)=2, find x.

int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a) 1/2(ln((x-1)/(x+1)))^2+C (b) 1/2(ln((x+1)/(x-1)))^2+C (c) 1/4(ln((x-1)/(x+1)))^2+C (d) 1/4(ln((x+1)/(x-1)))^2+C

int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a) 1/2(ln((x-1)/(x+1)))^2+C (b) 1/2(ln((x+1)/(x-1)))^2+C (c) 1/4(ln((x-1)/(x+1)))^2+C (d) 1/4(ln((x+1)/(x-1)))^2+C

int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a) 1/2(ln((x-1)/(x+1)))^2+C (b) 1/2(ln((x+1)/(x-1)))^2+C (c) 1/4(ln((x-1)/(x+1)))^2+C (d) 1/4(ln((x+1)/(x-1)))^2+C

If int1/((x^(2)-1))log((x-1)/(x+1))dx=A[log((x-1)/(x+1))]^(2)+c , then A =