erweitern ((x^{(3)}-1)(x+1)^{(3)})/(x+2)

Lösung

erweitern

\frac{( x ^{(3)} - 1 ) ( x + 1 ) ^{(3)}}{x + 2}

\frac{x ^{6} + 3 x ^{5} + 3 x ^{4} - 3 x ^{2} - 3 x - 1}{x + 2}

Schritte zur Lösung

\frac{( x ^{3} - 1 ) ( x + 1 ) ^{3}}{x + 2}

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

= \frac{( x ^{3} - 1 ) ( x ^{3} + 3 x ^{2} + 3 x + 1 )}{x + 2}

Multipliziere aus

(x^{3} - 1) (x^{3} + 3 x^{2} + 3 x + 1) : x^{6} + 3 x^{5} + 3 x^{4} - 3 x^{2} - 3 x - 1

= \frac{x ^{6} + 3 x ^{5} + 3 x ^{4} - 3 x ^{2} - 3 x - 1}{x + 2}

\frac{d}{d x} ((3 cos (x)) (ln (1 + x)))

\int \frac{7 sec ^{2} ( 2 x )}{3 - 5 tan ( 2 x )} d x

\int arcsinh (x) d x

x \to + 0 + lim (x^{12} ln (x))

\frac{d}{d x} (\frac{2}{2 x ^{4} - 5})