Question

Дан неопрелеленный интеграл. Найти интеграл

Answer 1

$t=ln(x+sqrt{1+x^2})=>dt=dfrac{1}{x+sqrt{1+x^2}}*(1+dfrac{1}{2sqrt{1+x^2}}*2x)dx=dfrac{1}{sqrt{1+x^2}}dx\ intdfrac{dx}{sqrt{(1+x^2)ln(x+sqrt{1+x^2})}}=intdfrac{1}{sqrt t}dt=2sqrt t + C=2sqrt{ln(x+sqrt{1+x^2})}+C$