Find the value of `int_(0)^(1)logxdx`.

Prove that int_0^1log(x/(1-x))dx=int_0^1log((1-x)/x)dx . Find the value of int_0^1log(x/(1-x))dx

Find the value of int_(0)^(1)3sqrt(2x^(3)-3x^(2)-x+1)dx .

If int_(-1)^(4)f(x)dx=4" and "int_(2)^(4)(3-f(x))dx=7 , then find the value of int_(2)^(-1)f(x)dx is

If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0 , then find the value of int_(0)^(a)(dx)/(1+f(x)) .

Find the value of int_(0)^(pi//2)sin2xlogtan xdx .

Find the value of int_0^(pi/2)sin^4x/(sin^4x+cos^4x)dx

The value of int_(0)^(oo)(xlnx)/((1+x^(2))^(2))dx is a) oo b) 1//2 c)2 d)0

The value of int_(0)^(6)|x-3|dx is equal to a)6 b)0 c)12 d)9