int_(a)^(b)(ln x)/(x)dx=

int_(a)^(b)(logx)/(x)dx=(1)/(2)log(ab)log((b)/(a))

int_(a)^(b) (log x)/(x) dx is :

int_(a)^(b)(log x)/(x)backslash dx=(1)/(2)log(ab)backslash log((b)/(a))

int_(1)^(3)(log x)/(x)dx

int_(1)^(2)(log x)/(x)dx=

int_(a)^(b)(log x)/(x^(2))dx

Prove that int_(a)^(b) f(x)dx= int_(a)^(b) f (a+b-x)dx" hence evaluate " int_(0)^(pi/4) log(1+tan x)dx .

Let f(x) = ln ((1-sinx)/(1+sinx)) , then show that int_(a)^(b) f(x)dx = int_(b)^(a) ln((1+sinx)/(1-sinx))dx .

Let f(x) = ln ((1-sinx)/(1+sinx)) , then show that int_(a)^(b) f(x)dx = int_(b)^(a) ln((1+sinx)/(1-sinx))dx .

If a=lim_(x rarr oo)(sin x)/(x)&b=lim_(x rarr0)(sin x)/(x) Then int_(a)^(b)(log(1+x))/(1+x^(2))dx is equal to