integral (2-3x^2)^3

Lösung

integral

(2 - 3 x^{2})^{3}

8 x - 12 x^{3} + \frac{54 x ^{5}}{5} - \frac{27 x ^{7}}{7} + C

Schritte zur Lösung

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

Multipliziere aus

(2 - 3 x^{2})^{3} : 8 - 36 x^{2} + 54 x^{4} - 27 x^{6}

= \int 8 - 36 x^{2} + 54 x^{4} - 27 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 8 d x - \int 36 x^{2} d x + \int 54 x^{4} d x - \int 27 x^{6} d x

\int 8 d x = 8 x

\int 36 x^{2} d x = 12 x^{3}

\int 54 x^{4} d x = \frac{54 x ^{5}}{5}

\int 27 x^{6} d x = \frac{27 x ^{7}}{7}

= 8 x - 12 x^{3} + \frac{54 x ^{5}}{5} - \frac{27 x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

= 8 x - 12 x^{3} + \frac{54 x ^{5}}{5} - \frac{27 x ^{7}}{7} + C

in t e g r a l \frac{1}{( x + 2 )}

in t e g r a l cos^{- 2} (x)

in t e g r a l 1 - cos (6 x)

in t e g r a l (5 x - 4)^{- 3}

in t e g r a l sin (y^{3})