`int_0^1 (log x)/(sqrt(1-x^2))dx`

Evaluate int_(0)^(1)(ln x)/(sqrt(1-x^(2)))dx

(i) int_0^1 (dx)/sqrt(1-x^2) (ii) int_0^1 (dx)/sqrt(1+x^2) (iii) a int_1^sqrt3 (dx)/(1+x^2) b int_0^1 (dx)/(1+x^2) (iv) int_0^(2//3) (dx)/(4+9x^2) (v) int_0^1 x/(x^2+1)dx (vi) int_2^3 x/(x^2+1) dx

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

int_-1^1 log(x+sqrt(x^2+1))dx

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

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

int_(0)^(1)(x^(2)ln x)/(sqrt(1-x^(2)))dx

int_0^1 log((x)/(1-x))dx=0

The value of int_(-1)^(1) (log(x+sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(x) dx-int_(-1)^(1) (log(x +sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(-x)dx ,

Show that : int_0^1(logx)/((1+x))dx=-int_0^1(log(1+x))/x dx