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Beliebt Rechnen >

integral of p(p+3)^8

Lösung

\int p (p + 3)^{8} d p

Lösung

\frac{( p + 3 ) ^{10}}{10} - \frac{( p + 3 ) ^{9}}{3} + C

Schritte zur Lösung

\int p (p + 3)^{8} d p

Wende U-Substitution an

= \int (u - 3) u^{8} d u

Multipliziere aus

(u - 3) u^{8} : u^{9} - 3 u^{8}

= \int u^{9} - 3 u^{8} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{9} d u - \int 3 u^{8} d u

\int u^{9} d u = \frac{u ^{10}}{10}

\int 3 u^{8} d u = \frac{u ^{9}}{3}

= \frac{u ^{10}}{10} - \frac{u ^{9}}{3}

Setze in

u = p + 3

ein

= \frac{( p + 3 ) ^{10}}{10} - \frac{( p + 3 ) ^{9}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{( p + 3 ) ^{10}}{10} - \frac{( p + 3 ) ^{9}}{3} + C

Graph

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