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

Lösung

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

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

Schritte zur Lösung

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

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

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

= x^{5} - (- \frac{5}{x})

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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