" 32.Let "u=int_(0)^(t)(ln(x+1))/(x^(2)+1)dx" and "v=int_(0)^( pi/2)ln(sin2x)dx" then "-

Let u=int_(0)^(1)(ln(x+1))/(x^(2)+1)dx and v=int_(0)^((pi)/(2))ln(sin2x)dx, thenu=-(pi)/(2)ln2(b)4u+v=0u+4v=0 (d) u=(pi)/(8)ln2

int_(0)^((pi)/(2))log(sin2x)dx

int_(0)^(1)(log(1+x))/(1+x^(2))dx

int_(0)^((pi)/(2))log(sin x)dx

Let u=int_0^1("ln"(x+1))/(x^2+1)dx a n d v=int_0^(pi/2)ln(sin2x)dx ,t h e n (a) u=-pi/2ln2 (b) 4u+v=0 (c) u+4v=0 (d) u=pi/8ln2

Let u=int_0^1("ln"(x+1))/(x^2+1)dxa n dv=int_0^(pi/2)ln(sin2x)dx ,t h e n u=-pi/2ln2 (b) 4u+v=0 u+4v=0 (d) u=pi/8ln2

int_(0)^(pi//2) log sin x dx =

int_(0)^( pi)cos2x*log(sin x)dx

int_(0)^(pi)log sin^(2)x dx=