- #1

Dell

- 590

- 0

using[tex]\int[/tex]udv=uv-[tex]\int[/tex]vdu

dv=dx

v=x

u=arctg[tex]\sqrt{x}[/tex]

du=u'dx=[1/(1+x)]dx

[tex]\int[/tex]arctg[tex]\sqrt{x}[/tex]dx=xarctg[tex]\sqrt{x}[/tex] - [tex]\int[/tex]x*[1/(1+x)]dx

=xarctg[tex]\sqrt{x}[/tex] - [tex]\int[/tex][x/(1+x)]dx

=xarctg[tex]\sqrt{x}[/tex] - [tex]\int[/tex]1-[1/(1+x)]dx

=

**xarctg[tex]\sqrt{x}[/tex] - x+ln|x+1|+c**

but this is wrong, where have i made the mistake?