[tex]\int[/tex]arctg[tex]\sqrt{x}[/tex]dx(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration, where have i gone wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**