integral of pi(x^2-x^4)

Lösung

\int π (x^{2} - x^{4}) d x

π (\frac{x ^{3}}{3} - \frac{x ^{5}}{5}) + C

Schritte zur Lösung

\int π (x^{2} - x^{4}) d x

Entferne die Konstante:

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

= π \cdot \int x^{2} - x^{4} 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

= π (\int x^{2} d x - \int x^{4} d x)

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

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

= π (\frac{x ^{3}}{3} - \frac{x ^{5}}{5})

Füge eine Konstante zur Lösung hinzu

= π (\frac{x ^{3}}{3} - \frac{x ^{5}}{5}) + C

\int \frac{sin ( ln ( y ) )}{y} d y

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ma c l a u r in \frac{1}{1 - x ^{3}}

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