integral of (x^4+x+9)

Lösung

\int (x^{4} + x + 9) d x

\frac{x ^{5}}{5} + \frac{x ^{2}}{2} + 9 x + C

Schritte zur Lösung

\int x^{4} + x + 9 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^{4} d x + \int x d x + \int 9 d x

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

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

\int 9 d x = 9 x

= \frac{x ^{5}}{5} + \frac{x ^{2}}{2} + 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + \frac{x ^{2}}{2} + 9 x + C

d er i v a t i v e ln (\frac{x ^{2} - 1}{x ^{2} + 1})

in v erse l a pl a ce \frac{s ^{2} + 1}{s ^{2} ( s + 2 )}

\frac{\partial}{\partial y} (e^{- x} sin (yz))

\frac{d}{d x} (\frac{x ^{2}}{( x ^{2} - 1 )})

t an g e n t f (x) = 4 - 3 ln (x), at x = 1