log[e^(x)((x-2)/(x+2))^(3/4)]

y=log[e^(3x)*((x-4)/(x+3))^(2/3)], find (dy)/(dx)

If y=tan^(-1)[(log(e//x^(3)))/(log(ex^(3)))]+tan^(-1)[(log(e^(4)x^(3)))/(log(e//x^(12)))]," then "(d^(2)y)/(dx^(2))=

A : (a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/(a))^(3)+....=log_(e)((a)/(b)) R : log_(e)(1-x)=-x-(x^(2))/(2)-(x^(3))/(3)-(x^(4))/(4)-....

If int_(log_(e^(2)))^(x)(e^(x)-1)^(-1)dx="log"_(e )(3)/(2) then the value of x is

If f((3t-4)/(3t+4))=t+2 then int f(x)dx= (A) e^(x-2)log((3x-4)/(3x+4))(B)-(8)/(3)log|1-x|+2(x)/(3)+c(C)(8)/(3)log|1-x|+(x)/(3)+c(D)e^(x+2)log|(1+x)/(1-x)|+c

Let a=int_0^(log2) (2e^(3x)+e^(2x)-1)/(e^(3x)+e^(2x)-e^x+1)dx , then 4e^a =

Let a=int_0^(log2) (2e^(3x)+e^(2x)-1)/(e^(3x)+e^(2x)-e^x+1)dx , then 4e^a =

int_(1)^(e)(x^(4)ln x+2)/(x^(3)ln x+x)dx=(e^(2)+a)/(b)-ln(e^(2)+1) where a and b are positive integers then (a)/(b)=

If f(x)=|{:(2^(-x),e^(x log_(e)2),x^(2)),(2^(-3x),e^(3x log_(e)2),x^(4)),(2^(-5x),e^(5x log_(e)2),1):}| then show that f(x) is symmetric about origin

The domain of the function f(x)=(log_(e)(log_((1)/(2))|x-3|))/(x^(2)-4x+3) is