integral of 2x^3y^4+x

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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