integral of (5x^5+3)x^2

Lösung

\int (5 x^{5} + 3) x^{2} d x

\frac{5 x ^{8}}{8} + x^{3} + C

Schritte zur Lösung

\int (5 x^{5} + 3) x^{2} d x

Multipliziere aus

(5 x^{5} + 3) x^{2} : 5 x^{7} + 3 x^{2}

= \int 5 x^{7} + 3 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 5 x^{7} d x + \int 3 x^{2} d x

\int 5 x^{7} d x = \frac{5 x ^{8}}{8}

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

= \frac{5 x ^{8}}{8} + x^{3}

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{8}}{8} + x^{3} + C

\int \frac{y ^{2} + 9}{y ^{2} + 4} d y

\frac{\partial}{\partial x} (e^{x} \cdot ln (y))

\frac{d}{d x} (\frac{3 x - 4}{x + 2})

\int \frac{1}{3 x - 1} d x

\int_{- 4}^{4} 4 - x^{2} d x