integral of 5x(x^4-1/5)

Lösung

\int 5 x (x^{4} - \frac{1}{5}) d x

5 (\frac{1}{10} x^{2} (5 x^{4} - 1) - \frac{x ^{6}}{3}) + C

Schritte zur Lösung

\int 5 x (x^{4} - \frac{1}{5}) d x

Entferne die Konstante:

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

= 5 \cdot \int x (x^{4} - \frac{1}{5}) d x

Wende die partielle Integration an

= 5 (\frac{1}{10} x^{2} (5 x^{4} - 1) - \int 2 x^{5} d x)

\int 2 x^{5} d x = \frac{x ^{6}}{3}

= 5 (\frac{1}{10} x^{2} (5 x^{4} - 1) - \frac{x ^{6}}{3})

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{1}{10} x^{2} (5 x^{4} - 1) - \frac{x ^{6}}{3}) + C

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