integral of x^4(1-x^2)

Lösung

\int x^{4} (1 - x^{2}) d x

\frac{x ^{5}}{5} - \frac{x ^{7}}{7} + C

Schritte zur Lösung

\int x^{4} (1 - x^{2}) d x

Multipliziere aus

x^{4} (1 - x^{2}) : x^{4} - x^{6}

= \int x^{4} - x^{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 x^{4} d x - \int x^{6} d x

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

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

= \frac{x ^{5}}{5} - \frac{x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

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

ma c l a u r in f (x) = \frac{1}{( 1 + x )} 1

x^{^{'}} - a x - 1 = 0

\int_{0}^{1} x \cdot 3^{x^{2} + 1} d x

y^{^{''}} + 9 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial x} (x^{3} + x e^{y} - 2 y)