" If "a,b,>0," then "int_(1)^(a)(1)/(x)dx+int_(1)^(b)(1)/(x)dx=

If a, b, gt 0 , then int_(1)^(a)(1)/(x)dx + int_(1)^(b)(1)/(x)dx=

int_(0)^(1)(1)/(1+x)dx=

int_(a)^(b)(1)/(x^(2))dx

int_(0)^(1)(x)/(x+1)dx=

int_(a)^(b)(|1-x|)/(1-x)dx=

int_(0)^(1)x sin(x-1)dx+int_(0)^(1)(1-x)sin xdx=

Let n in N such that n gt 1 . Statement-1: int_(oo)^(0) (1)/(1+x^(n))dx=int_(0)^(1) (1)/((1-x^(n))^(1//n))dx Statement-2: int_a^b f(x)dx=int_(a)^(b) f(a+b-x)dx

Prove that int_(0)^(1)log((x)/(x-1))dx=int_(0)^(1)log((x-1)/(x))dx . Find the value of int_(0)^(1)log((x)/(x-1))dx

Show that :int_(0)^(1)(log x)/((1+x))dx=-int_(0)^(1)(log(1+x))/(x)dx