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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{( 2 + x )})

\frac{d}{d x} (\frac{x ^{2}}{y ^{2}})

\frac{d}{d x} (\frac{sin ( x )}{2 + cos ( x )})

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

x \to 1 lim (6 2 - x)