integral (x-1)(x+3)^3

Lösung

integral

(x - 1) (x + 3)^{3}

\frac{x ^{5}}{5} + 2 x^{4} + 6 x^{3} - 27 x + C

Schritte zur Lösung

\int (x - 1) (x + 3)^{3} d x

Multipliziere aus

(x - 1) (x + 3)^{3} : x^{4} + 8 x^{3} + 18 x^{2} - 27

= \int x^{4} + 8 x^{3} + 18 x^{2} - 27 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 x^{4} d x + \int 8 x^{3} d x + \int 18 x^{2} d x - \int 27 d x

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

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

\int 18 x^{2} d x = 6 x^{3}

\int 27 d x = 27 x

= \frac{x ^{5}}{5} + 2 x^{4} + 6 x^{3} - 27 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} + 2 x^{4} + 6 x^{3} - 27 x + C

in t e g r a l (e^{y})^{2}

in t e g r a l \frac{1}{( x ^{3} + x ^{2} + x )}

in t e g r a l \frac{1}{( x ^{2} - 1 )}

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in t e g r a l - sin^{2} (x) + tan^{2} (x)