∫dt/(1-2t^2)=(-1/2)∫dt/{t^2-(1/2)}
=(-1/(2√2))∫dt/{t-(1/√2)}-(-1/(2√2))∫dt/{t+(1/√2)}
=(-1/(2√2))log|t-(1/√2)|-(-1/(2√2))log|t+(1/√2)|+C
=(-1/(2√2))log|(t-(1/√2))/(t+(1/√2))|+C
=(1/(2√2))log|(t+(1/√2))/(t-(1/√2))|+C
=(1/(2√2))log|((√2)(x/√(1+x^2))+1)/((√2)(x/√(1+x^2))-1)|+C
=(1/(2√2))log|((√2)x+√(1+x^2))/((√2)x-√(1+x^2))|+C
=((√2)/4)log|(√(1+x^2)+(√2)x)/(√(1+x^2)-(√2)x)|+C