integral of 2x+4x^2-5/2

Lösung

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

x^{2} + \frac{4 x ^{3}}{3} - \frac{5}{2} x + C

Schritte zur Lösung

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

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

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

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

= x^{2} + \frac{4 x ^{3}}{3} - \frac{5}{2} x

Füge eine Konstante zur Lösung hinzu

= x^{2} + \frac{4 x ^{3}}{3} - \frac{5}{2} x + C

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

x \to 0 lim (\frac{- 1}{14 x})

d er i v a t i v e y = 6 x^{2} sin (x) tan (x)

x \to 2 lim (\frac{2 x + 4}{x - 2})

\int 4 x^{2} sin (x) d x