integral of x^3-1/2 x^2+4

Lösung

\int x^{3} - \frac{1}{2} x^{2} + 4 d x

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

Schritte zur Lösung

\int x^{3} - \frac{1}{2} x^{2} + 4 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 x^{3} d x - \int \frac{1}{2} x^{2} d x + \int 4 d x

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

\int \frac{1}{2} x^{2} d x = \frac{x ^{3}}{6}

\int 4 d x = 4 x

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

Füge eine Konstante zur Lösung hinzu

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

t an g e n t f (x) = e^{x} (x^{4} + 3), (0, 3)

\frac{d}{d x} (\frac{x ^{2} - 10 x + 9}{( x - 5 ) ^{2}})

d er i v a t i v e f (x) = \frac{4}{2 - x}

d er i v a t i v e - \frac{36 ( x - 1 )}{( x + 3 ) ^{3}}

a re a 2 x^{2} + 5, - 2, 3