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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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 y^{2} d y + \int 14 y^{3} d y + \int y^{4} d y

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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