integral of ((28t^7-8)/t)

Lösung

\int (\frac{28 t ^{7} - 8}{t}) d t

4 t^{7} - 8 ln ∣ t ∣ + C

Schritte zur Lösung

\int \frac{28 t ^{7} - 8}{t} d t

Multipliziere aus

\frac{28 t ^{7} - 8}{t} : 28 t^{6} - \frac{8}{t}

= \int 28 t^{6} - \frac{8}{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 28 t^{6} d t - \int \frac{8}{t} d t

\int 28 t^{6} d t = 4 t^{7}

\int \frac{8}{t} d t = 8 ln ∣ t ∣

= 4 t^{7} - 8 ln ∣ t ∣

Füge eine Konstante zur Lösung hinzu

= 4 t^{7} - 8 ln ∣ t ∣ + C

\int (4 - x^{\frac{2}{3}})^{3} d x

\int \frac{1}{x ( x - 2 ) ^{3}} d x

\int (tan (x) + sin (x)) cos (x) d x

\int 15 sin^{4} (3 x) cos (3 x) d x

\int x^{7} - 6 x + 8 d x