√x=t
x=t²
dx=2tdt
∫arctan√xdx
=∫2tarctantdt
=∫arctantdt²
=t²arctant-∫t²/(1+t²)dt
=t²arctant-∫(1+t²-1)/(1+t²)dt
=t²arctant-∫1-1/(1+t²)dt
=t²arctant-t+∫1/(1+t²)dt
=t²arctant-t+arctant+C
=xarctan√x-√x+arctan√x+C
√x=t
x=t²
dx=2tdt
∫arctan√xdx
=∫2tarctantdt
=∫arctantdt²
=t²arctant-∫t²/(1+t²)dt
=t²arctant-∫(1+t²-1)/(1+t²)dt
=t²arctant-∫1-1/(1+t²)dt
=t²arctant-t+∫1/(1+t²)dt
=t²arctant-t+arctant+C
=xarctan√x-√x+arctan√x+C