integral of 2x^3+4x+5

Lösung

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

\frac{x ^{4}}{2} + 2 x^{2} + 5 x + C

Schritte zur Lösung

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

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

\int 4 x d x = 2 x^{2}

\int 5 d x = 5 x

= \frac{x ^{4}}{2} + 2 x^{2} + 5 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{2} + 2 x^{2} + 5 x + C

x \to π lim (sin (\frac{11}{6}))

d er i v a t i v e \frac{1}{8} x^{4} - \frac{32}{x ^{3}}

\int_{- 4 π}^{4 π} (sin^{2} (x) + 1) d x

a re a x^{3} - 11 x^{2} + 28 x, - x^{3} + 11 x^{2} - 28 x

y^{^{'}} = e^{x^{2}}