integral ((1-x^3))/((1-x))

Lösung

integral

\frac{( 1 - x ^{3} )}{( 1 - x )}

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

Schritte zur Lösung

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

Vereinfache

\frac{1 - x ^{3}}{1 - x} : x^{2} + x + 1

= \int x^{2} + x + 1 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^{2} d x + \int x d x + \int 1 d x

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

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

\int 1 d x = x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

in t e g r a l \frac{1}{( 1 + lo g _{10} ( x ) )}

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

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

in t e g r a l lo g_{10} (x^{2} + 4)

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