integral of 2x^3+5x^2-2x+pi

Lösung

\int 2 x^{3} + 5 x^{2} - 2 x + π d x

\frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + π x + C

Schritte zur Lösung

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

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

\int π d x = π x

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + π x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + π x + C

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