Sustitución trigonométrica integral indefinida sinsunt

Sea x=sinu, dx=cosudu∫dx/(x √(1-x^2))=∫cosudu/(sinu cosu)=1/2∫(cosu sinu cosu-sinu)du /(sinu cosu)=1/2∫[1 (cosu-sinu)/(sinu cosu)]du=1/2[u ln|sinu cosu|] C=1/2arcsinx 1/2ln|x √(1- x^2)|