\int 1/2*sqrt(x) dx = sqrt(x) - Why?
I cannot understand how the author got this? Could you explain ...
Given a real [or even complex...] $\displaystyle \alpha$ is...
$\displaystyle \frac{d}{dx} x^{\alpha} = \alpha\ x^{\alpha-1}$ (1)
... and from (1) $\displaystyle \forall \alpha \ne -1$ You derive...
$\displaystyle \int x^{\alpha}\ dx = \frac{x^{\alpha+1}}{\alpha+1} + c $ (2)
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$