integral of (1/(t^2)+sqrt(t))

Lösung

\int (\frac{1}{t ^{2}} + t) d t

- \frac{1}{t} + \frac{2}{3} t^{\frac{3}{2}} + C

Schritte zur Lösung

\int \frac{1}{t ^{2}} + t d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{t ^{2}} d t + \int t d t

\int \frac{1}{t ^{2}} d t = - \frac{1}{t}

\int t d t = \frac{2}{3} t^{\frac{3}{2}}

= - \frac{1}{t} + \frac{2}{3} t^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{t} + \frac{2}{3} t^{\frac{3}{2}} + C

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