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Beliebt Rechnen >

integral of (x-3)(x+11)^{15}

Lösung

\int (x - 3) (x + 11)^{15} d x

Lösung

\frac{( x + 11 ) ^{17}}{17} - \frac{7 ( x + 11 ) ^{16}}{8} + C

Schritte zur Lösung

\int (x - 3) (x + 11)^{15} d x

Wende U-Substitution an

= \int u^{15} (u - 14) d u

Multipliziere aus

u^{15} (u - 14) : u^{16} - 14 u^{15}

= \int u^{16} - 14 u^{15} 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^{16} d u - \int 14 u^{15} d u

\int u^{16} d u = \frac{u ^{17}}{17}

\int 14 u^{15} d u = \frac{7 u ^{16}}{8}

= \frac{u ^{17}}{17} - \frac{7 u ^{16}}{8}

Setze in

u = x + 11

ein

= \frac{( x + 11 ) ^{17}}{17} - \frac{7 ( x + 11 ) ^{16}}{8}

Füge eine Konstante zur Lösung hinzu

= \frac{( x + 11 ) ^{17}}{17} - \frac{7 ( x + 11 ) ^{16}}{8} + C

Graph

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