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Beliebt Rechnen >

integral 4x^2+3x+2*2(x+1)

Lösung

integral

4 x^{2} + 3 x + 2 \cdot 2 (x + 1)

Lösung

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

Schritte zur Lösung

\int 4 x^{2} + 3 x + 2 \cdot 2 (x + 1) d x

Vereinfache

4 x^{2} + 3 x + 2 \cdot 2 (x + 1) : 4 x^{2} + 7 x + 4

= \int 4 x^{2} + 7 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 4 x^{2} d x + \int 7 x d x + \int 4 d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 4 d x = 4 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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