Задача 35227 ln(x+sqrt(1+x^2))dx...

bekmurod

2019-04-02 13:42:05

ln(x+sqrt(1+x^2))dx

sova

2019-04-02 15:50:57

Интегрируем по частям:
ln(x+sqrt(1+x^2))=u
dx=dv

du=dx/sqrt(1+x^2)
v=x

∫ ln(x+sqrt(1+x^2)dx=x*ln(x+sqrt(1+x^2)) - ∫ xdx/sqrt(1+x^2)=

=x*ln(x+sqrt(1+x^2)) -(1/2)*2sqrt(1+x^2) + C=

= [b]x*ln(x+sqrt(1+x^2)) -sqrt(1+x^2) +C[/b]