Find the integral
$$I=\int\dfrac{\sqrt{\ln{(x+\sqrt{x^2+1})}}}{1+x^2}dx$$
My try: let $$x=\tan{t}$$ $$I=\int\sqrt{\ln{(\tan{t}+\sec{t})}}dt$$ note $$\tan{t}+\sec{t}=\dfrac{\sin{t}}{\cos{t}}+\dfrac{1}{\cos{t}}=\dfrac{\sin{\dfrac{t}{2}}+\cos{\dfrac{t}{2}}}{\cos{\dfrac{t}{2}}-\sin{\dfrac{t}{2}}}=\tan{\left(\dfrac{t}{2}+\dfrac{\pi}{4}\right)}$$then I can't,Thank you