integral of x(4x+5)^3

Lösung

\int x (4 x + 5)^{3} d x

\frac{64 x ^{5}}{5} + 60 x^{4} + 100 x^{3} + \frac{125 x ^{2}}{2} + C

Schritte zur Lösung

\int x (4 x + 5)^{3} d x

Multipliziere aus

x (4 x + 5)^{3} : 64 x^{4} + 240 x^{3} + 300 x^{2} + 125 x

= \int 64 x^{4} + 240 x^{3} + 300 x^{2} + 125 x 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 64 x^{4} d x + \int 240 x^{3} d x + \int 300 x^{2} d x + \int 125 x d x

\int 64 x^{4} d x = \frac{64 x ^{5}}{5}

\int 240 x^{3} d x = 60 x^{4}

\int 300 x^{2} d x = 100 x^{3}

\int 125 x d x = \frac{125 x ^{2}}{2}

= \frac{64 x ^{5}}{5} + 60 x^{4} + 100 x^{3} + \frac{125 x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{64 x ^{5}}{5} + 60 x^{4} + 100 x^{3} + \frac{125 x ^{2}}{2} + C

im pl i c i t \frac{d y}{d x}, x y = 28

s l o p e (- 1.2) (- 2.3)

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