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Beliebt Rechnen >

integral of (12t^8-t)/(t^3)

Lösung

\int \frac{12 t ^{8} - t}{t ^{3}} d t

Lösung

2 t^{6} + \frac{1}{t} + C

Schritte zur Lösung

\int \frac{12 t ^{8} - t}{t ^{3}} d t

Multipliziere aus

\frac{12 t ^{8} - t}{t ^{3}} : 12 t^{5} - \frac{1}{t ^{2}}

= \int 12 t^{5} - \frac{1}{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 12 t^{5} d t - \int \frac{1}{t ^{2}} d t

\int 12 t^{5} d t = 2 t^{6}

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

= 2 t^{6} - (- \frac{1}{t})

Vereinfache

= 2 t^{6} + \frac{1}{t}

Füge eine Konstante zur Lösung hinzu

= 2 t^{6} + \frac{1}{t} + C

Graph

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