[" 2."((log x)^(2))/(x)],[" Ans.Putting "log x=t]

int _(2) ^(4) (log x ^(2))/( log x ^(2) + log (36-12 x + x ^(2)) dx is

Derivative of (log x) ^(x) w.r.t log x is

Derivative of (log x) ^(x) w.r.t log x is

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

[" (v) Differentiate "log[(sqrt(1+x^(2))+x)/(sqrt(1+x^(2))-x)]" w.r.t."],[cos(log x)]

The value of x satisfies the equation (1-2(log x^(2)))/(log x-2(log x)^(2))=1

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

log(1+x^(2))"w.r.t."tan^(-1)x

Derivative of (log x)^x w.r.t. log x is