integral of (3x^4-5x^2+x)

Lösung

\int (3 x^{4} - 5 x^{2} + x) d x

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

Schritte zur Lösung

\int 3 x^{4} - 5 x^{2} + 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 3 x^{4} d x - \int 5 x^{2} d x + \int x d x

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

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

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

Füge eine Konstante zur Lösung hinzu

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

t a y l or arctan (x^{2}), 0

\frac{d}{d x} (lo g_{a} (- x^{2} - x))

\frac{d}{d x} ((e^{3 x} - 1)^{5})

d er i v a t i v e y = ln (ln (\frac{1}{x}))

t an g e n t f (x) = 2 x^{2} + 8 x - 2