integral of x(4x+1)

Lösung

\int x (4 x + 1) d x

\frac{4 x ^{3}}{3} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int x (4 x + 1) d x

Multipliziere aus

x (4 x + 1) : 4 x^{2} + x

= \int 4 x^{2} + 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 4 x^{2} d x + \int x d x

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

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

= \frac{4 x ^{3}}{3} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

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

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