integral of x^2(7+x)^2

Lösung

\int x^{2} (7 + x)^{2} d x

\frac{49 x ^{3}}{3} + \frac{7 x ^{4}}{2} + \frac{x ^{5}}{5} + C

Schritte zur Lösung

\int x^{2} (7 + x)^{2} d x

Multipliziere aus

x^{2} (7 + x)^{2} : 49 x^{2} + 14 x^{3} + x^{4}

= \int 49 x^{2} + 14 x^{3} + x^{4} 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 49 x^{2} d x + \int 14 x^{3} d x + \int x^{4} d x

\int 49 x^{2} d x = \frac{49 x ^{3}}{3}

\int 14 x^{3} d x = \frac{7 x ^{4}}{2}

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

= \frac{49 x ^{3}}{3} + \frac{7 x ^{4}}{2} + \frac{x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{49 x ^{3}}{3} + \frac{7 x ^{4}}{2} + \frac{x ^{5}}{5} + C

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