integral (1-x^2)^3

Lösung

integral

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

x - x^{3} + \frac{3 x ^{5}}{5} - \frac{x ^{7}}{7} + C

Schritte zur Lösung

\int (1 - x^{2})^{3} d x

Multipliziere aus

(1 - x^{2})^{3} : 1 - 3 x^{2} + 3 x^{4} - x^{6}

= \int 1 - 3 x^{2} + 3 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 1 d x - \int 3 x^{2} d x + \int 3 x^{4} d x - \int x^{6} d x

\int 1 d x = x

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

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

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

= x - x^{3} + \frac{3 x ^{5}}{5} - \frac{x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

= x - x^{3} + \frac{3 x ^{5}}{5} - \frac{x ^{7}}{7} + C

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

in t e g r a l \frac{e ^{\frac{1}{y}}}{y}

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

in t e g r a l x^{3} - x^{2}

in t e g r a l \frac{1}{( x + 1 ) ^{3}}