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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

(1 + \frac{1}{t}) \frac{1}{t ^{2}} : \frac{t + 1}{t ^{3}}

= \int \frac{t + 1}{t ^{3}} d t

Multipliziere aus

\frac{t + 1}{t ^{3}} : \frac{1}{t ^{2}} + \frac{1}{t ^{3}}

= \int \frac{1}{t ^{2}} + \frac{1}{t ^{3}} 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 \frac{1}{t ^{3}} d t

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

\int \frac{1}{t ^{3}} d t = - \frac{1}{2 t ^{2}}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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