integral of (3-4x^3+6x^6)/(x^6)

Lösung

\int \frac{3 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} d x

- \frac{3}{5 x ^{5}} + \frac{2}{x ^{2}} + 6 x + C

Schritte zur Lösung

\int \frac{3 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} d x

Multipliziere aus

\frac{3 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} : \frac{3}{x ^{6}} - \frac{4}{x ^{3}} + 6

= \int \frac{3}{x ^{6}} - \frac{4}{x ^{3}} + 6 d x

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{3}{x ^{6}} d x - \int \frac{4}{x ^{3}} d x + \int 6 d x

\int \frac{3}{x ^{6}} d x = - \frac{3}{5 x ^{5}}

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

\int 6 d x = 6 x

= - \frac{3}{5 x ^{5}} - (- \frac{2}{x ^{2}}) + 6 x

Vereinfache

= - \frac{3}{5 x ^{5}} + \frac{2}{x ^{2}} + 6 x

Füge eine Konstante zur Lösung hinzu

= - \frac{3}{5 x ^{5}} + \frac{2}{x ^{2}} + 6 x + C

- y^{^{'''}} + 2 y^{^{''}} + 3 y^{^{'}} + 3 = 0

\frac{d}{d x} (ln (x + 2 y))

\frac{d}{d x} (cot (11 x))

\int_{2}^{5} 4 d x

d er i v a t i v e y = \frac{7 x}{x}