integral of (u+u^4)

Lösung

\int (u + u^{4}) d u

\frac{u ^{2}}{2} + \frac{u ^{5}}{5} + C

Schritte zur Lösung

\int u + u^{4} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u + \int u^{4} d u

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

\int u^{4} d u = \frac{u ^{5}}{5}

= \frac{u ^{2}}{2} + \frac{u ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{u ^{2}}{2} + \frac{u ^{5}}{5} + C

\int_{1}^{1000} \frac{33}{x ^{3}} d x

\int_{- 5}^{5} (25 - x^{2}) d x

\int \frac{x}{16} d x

\frac{\partial}{\partial x} (\frac{2 x + y}{y - x})

\int \frac{64 x ^{2}}{x ^{4} - 40 x ^{2} + 144} d x