`int_(0)^(1)ln(1+x^(2))*dx`

sum_(n=1)^(oo)(1)/(n^(2))=(pi^(2))/(6) and int_(0)^(1)(ln x)/(1-x^(2))dx=-(pi^(2))/(lambda)

Evaluate int_(5)^(7)ln(x-3)^(2)dx+2int_(0)^(1)ln(x+4)^(2)dx

Evaluate the following integral: int_(0)^(1)log(1+x)dx

int_(0)^(oo)((ln(1+x^(2)))/(1+x^(2)))dx .

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

If int_(0)^(1)((1-x^(2))/(1+x^(2)+x^(4)))dx=a ln b, then

If I_(1)=int_(0)^(2pi)sin^(3)xdx and I_(2)=int_(0)^(1)ln((1)/(x)-1)dx , then

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

Evaluate the following definite integrals: int_(0)^(1)x log(1+x/2)dx

int_(0)^(1)(x-1)/(ln x)dx