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Beliebt Rechnen >

integral of xos(8x^2+pi)

Lösung

\int x os (8 x^{2} + π) d x

Lösung

os (\frac{π x ^{2}}{2} + 2 x^{4}) + C

Schritte zur Lösung

\int x os (8 x^{2} + π) d x

Entferne die Konstante:

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

= os \cdot \int (π + 8 x^{2}) x d x

Multipliziere aus

(π + 8 x^{2}) x : π x + 8 x^{3}

= os \cdot \int π x + 8 x^{3} 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

= os (\int π x d x + \int 8 x^{3} d x)

\int π x d x = \frac{π x ^{2}}{2}

\int 8 x^{3} d x = 2 x^{4}

= os (\frac{π x ^{2}}{2} + 2 x^{4})

Füge eine Konstante zur Lösung hinzu

= os (\frac{π x ^{2}}{2} + 2 x^{4}) + C

Graph

Beliebte Beispiele

derivative of (x^2+4x+6^5)

\frac{d}{d x} ((x^{2} + 4 x + 6)^{5})

\int 24

derivative y= 1/4 (6t^2+8)

d er i v a t i v e y = \frac{1}{4} (6 t^{2} + 8)

integral of 1/6 (e^{6x})

\int \frac{1}{6} (e^{6 x}) d x

derivative y=cos(e^x)

d er i v a t i v e y = cos (e^{x})