integral of (-4x^6+6x^4+3x^3+6)

Lösung

\int (- 4 x^{6} + 6 x^{4} + 3 x^{3} + 6) d x

- \frac{4 x ^{7}}{7} + \frac{6 x ^{5}}{5} + \frac{3 x ^{4}}{4} + 6 x + C

Schritte zur Lösung

\int - 4 x^{6} + 6 x^{4} + 3 x^{3} + 6 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^{6} d x + \int 6 x^{4} d x + \int 3 x^{3} d x + \int 6 d x

\int 4 x^{6} d x = \frac{4 x ^{7}}{7}

\int 6 x^{4} d x = \frac{6 x ^{5}}{5}

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

\int 6 d x = 6 x

= - \frac{4 x ^{7}}{7} + \frac{6 x ^{5}}{5} + \frac{3 x ^{4}}{4} + 6 x

Füge eine Konstante zur Lösung hinzu

= - \frac{4 x ^{7}}{7} + \frac{6 x ^{5}}{5} + \frac{3 x ^{4}}{4} + 6 x + C

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