Den antideriverte og ubestemte integral

Oppgave 4

Regn ut $\displaystyle \int \frac{1}{\sqrt{x}} dx$.

Løsning

\begin{align*} \int \frac{1}{\sqrt{x}} dx &= \int \frac{1}{x^{\frac{1}{2}}} dx = \int x^{-\frac{1}{2}} \ dx = \frac{1}{-\frac{1}{2}+1}x^{-\frac{1}{2} + 1} + C \\ &= \frac{1}{\frac{1}{2}}x^{\frac{1}{2}} + C = \underline{\underline{2 \sqrt{x} + C}} \end{align*}