integrate∫log[x+​sq root(x^2+1)]/sq root(1-x^2) dx

we know that ln(a/b)=lna-lnb

so separate and write ln(x+root(1+x^2)) – 1/2*ln(1-x^2)

now both of these integrals can be solved by using integration by parts and letting the second function as 1 and first function as the logarithmic one. after that the integrals turn into standard forms.