integral of x+x^2

Lösung

\int x + x^{2} d x

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int 5 x^{3} d x

\frac{d}{d x} ((1 + sin (x)) cos (2 x))

n = 0 \sum \infty \frac{5 n}{2 n - 1}

y^{^{'}} + 3 y = e^{- 3 x}

\int_{2}^{3} (4 + 2 x)^{2} d x