integral of x^4(x^2-3x)^2

Lösung

\int x^{4} (x^{2} - 3 x)^{2} d x

\frac{x ^{9}}{9} - \frac{3 x ^{8}}{4} + \frac{9 x ^{7}}{7} + C

Schritte zur Lösung

\int x^{4} (x^{2} - 3 x)^{2} d x

Multipliziere aus

x^{4} (x^{2} - 3 x)^{2} : x^{8} - 6 x^{7} + 9 x^{6}

= \int x^{8} - 6 x^{7} + 9 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^{8} d x - \int 6 x^{7} d x + \int 9 x^{6} d x

\int x^{8} d x = \frac{x ^{9}}{9}

\int 6 x^{7} d x = \frac{3 x ^{8}}{4}

\int 9 x^{6} d x = \frac{9 x ^{7}}{7}

= \frac{x ^{9}}{9} - \frac{3 x ^{8}}{4} + \frac{9 x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{9}}{9} - \frac{3 x ^{8}}{4} + \frac{9 x ^{7}}{7} + C

\int \frac{- sin ( x )}{cos ( x )} d x

\int \frac{2 x}{x ^{2} - 4} d x

\int 2 e^{- 2 x} sin (2 x) d x

\frac{d y}{d x} - 2 y tan (x) = y^{2} tan^{2} (x)

d er i v a t i v e f (x) = \frac{x ^{2}}{e ^{x}}