How Can I Evaluate This Integral: $\int_0^1 \frac{dx} {x+\sqrt{1-x^2}}$? Can someone help me with this integration question 
$$\int_0^1 \frac{dx} {x+\sqrt{1-x^2}} $$ 
I tried substitution with x=sinx and also tries times both denominator and numerator by 
$$ x- \sqrt {1-x^2} $$
but it becomes even more complicated. Can someone gives me a hint how to solve this question please?

Set $x=\sin y$
Then apply $$I=\int_a^bf(x)\ dx=\int_a^bf(a+b-x)\ dx$$
$$I+I=\int_a^bf(x)\ dx+\int_a^bf(a+b-x)\ dx$$
