integral of (1/4 x^6-5x^3+9x)

Lösung

\int (\frac{1}{4} x^{6} - 5 x^{3} + 9 x) d x

\frac{x ^{7}}{28} - \frac{5 x ^{4}}{4} + \frac{9 x ^{2}}{2} + C

Schritte zur Lösung

\int \frac{1}{4} x^{6} - 5 x^{3} + 9 x 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{1}{4} x^{6} d x - \int 5 x^{3} d x + \int 9 x d x

\int \frac{1}{4} x^{6} d x = \frac{x ^{7}}{28}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 9 x d x = \frac{9 x ^{2}}{2}

= \frac{x ^{7}}{28} - \frac{5 x ^{4}}{4} + \frac{9 x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{7}}{28} - \frac{5 x ^{4}}{4} + \frac{9 x ^{2}}{2} + C

x \to 0 lim (\frac{∣ x ( h + 1 ) ∣}{x})

d er i v a t i v e x + \frac{5}{x}

\int_{0}^{1} \frac{10}{4 y - 1} d y

x \to - 1 lim (ln (x))

d er i v a t i v e y = sin^{2} (x^{3})