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Beliebt Rechnen >

integral of sqrt(t)+1/(t^3)+7/(t^2)

Lösung

\int t + \frac{1}{t ^{3}} + \frac{7}{t ^{2}} d t

Lösung

\frac{2}{3} t^{\frac{3}{2}} - \frac{1}{2 t ^{2}} - \frac{7}{t} + C

Schritte zur Lösung

\int t + \frac{1}{t ^{3}} + \frac{7}{t ^{2}} 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 t d t + \int \frac{1}{t ^{3}} d t + \int \frac{7}{t ^{2}} d t

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

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

\int \frac{7}{t ^{2}} d t = - \frac{7}{t}

= \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{2 t ^{2}} - \frac{7}{t}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} t^{\frac{3}{2}} - \frac{1}{2 t ^{2}} - \frac{7}{t} + C

Graph

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