# Math Help - solving an indefinite integral

1. ## solving an indefinite integral

\int 1/2*sqrt(x) dx = sqrt(x) - Why?

I cannot understand how the author got this? Could you explain ...

2. Given a real [or even complex...] $\alpha$ is...

$\frac{d}{dx} x^{\alpha} = \alpha\ x^{\alpha-1}$ (1)

... and from (1) $\forall \alpha \ne -1$ You derive...

$\int x^{\alpha}\ dx = \frac{x^{\alpha+1}}{\alpha+1} + c$ (2)

Kind regards

$\chi$ $\sigma$

3. WHAT? nothing understandable

Do you understand that $\frac{{d\left( {\sqrt x } \right)}}{{dx}} = \frac{1}{{2\sqrt x }}~?$