Using property of define integrals, prove that :
`int_(0)^(1) (log(1+x))/(1+x^(2))=(pi)/8log2`

Using property of define integrals, prove that : int_(0)^(1) log(1/x-1)dx=0

Using property of define integrals, prove that : int_(0)^(pi//2)logcos x dx=(-pi)/2log2

Using property of define integrals, prove that : int_(0)^(pi//2)sin2xlogtanx dx=0

The value of int_(0)^(1)(8log(1+x))/(1+x^(2))dx is

int_(0)^(1)(2x)/(5x^(2)+1)dx=log6

Using properties of definite integral prove that int_0^2 xsqrt(2-x)dx= (16sqrt2)/15

Using properties of definite integrals, show that int_(0)^(pi//2)(xdx)/(sinx+cosx)=(pi)/(2sqrt(2))log(sqrt(2)+1)

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+tan^(3)x)dx=(pi)/4

Evaluate: int_(0)^(1) log ((1)/(x)-1)dx