integral of 1 (x^6-3ln(x)+1/x)

Lösung

\int \frac{d}{1} (x^{6} - 3 ln (x) + \frac{1}{x}) d x

d (\frac{x ^{7}}{7} - 3 (x ln (x) - x) + ln ∣ x ∣) + C

Schritte zur Lösung

\int \frac{d}{1} (x^{6} - 3 ln (x) + \frac{1}{x}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= d \cdot \int x^{6} - 3 ln (x) + \frac{1}{x} 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

= d (\int x^{6} d x - \int 3 ln (x) d x + \int \frac{1}{x} d x)

\int x^{6} d x = \frac{x ^{7}}{7}

\int 3 ln (x) d x = 3 (x ln (x) - x)

\int \frac{1}{x} d x = ln ∣ x ∣

= d (\frac{x ^{7}}{7} - 3 (x ln (x) - x) + ln ∣ x ∣)

Füge eine Konstante zur Lösung hinzu

= d (\frac{x ^{7}}{7} - 3 (x ln (x) - x) + ln ∣ x ∣) + C

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