integral of (x^4-4x^3+5/(x^2))

Lösung

\int (x^{4} - 4 x^{3} + \frac{5}{x ^{2}}) d x

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

Schritte zur Lösung

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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