erweitern (((n^2x^2-2)sin(nx)+2nxcos(nx)))/(n^3)

Lösung

erweitern

\frac{( ( n ^{2} x ^{2} - 2 ) sin ( n x ) + 2 n x cos ( n x ) )}{n ^{3}}

\frac{x ^{2} sin ( n x )}{n} - \frac{2 sin ( n x )}{n ^{3}} + \frac{2 x cos ( n x )}{n ^{2}}

Schritte zur Lösung

\frac{( n ^{2} x ^{2} - 2 ) sin ( n x ) + 2 n x cos ( n x )}{n ^{3}}

Multipliziere aus

(n^{2} x^{2} - 2) sin (n x) + 2 n x cos (n x) : n^{2} x^{2} sin (n x) - 2 sin (n x) + 2 n x cos (n x)

= \frac{n ^{2} x ^{2} sin ( n x ) - 2 sin ( n x ) + 2 n x cos ( n x )}{n ^{3}}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{n ^{2} x ^{2} sin ( n x ) - 2 sin ( n x ) + 2 n x cos ( n x )}{n ^{3}} = \frac{n ^{2} x ^{2} sin ( n x )}{n ^{3}} - \frac{2 sin ( n x )}{n ^{3}} + \frac{2 n x cos ( n x )}{n ^{3}}

= \frac{n ^{2} x ^{2} sin ( n x )}{n ^{3}} - \frac{2 sin ( n x )}{n ^{3}} + \frac{2 n x cos ( n x )}{n ^{3}}

Streiche

\frac{n ^{2} x ^{2} sin ( n x )}{n ^{3}} : \frac{x ^{2} sin ( n x )}{n}

= \frac{x ^{2} sin ( n x )}{n} - \frac{2 sin ( n x )}{n ^{3}} + \frac{2 n x cos ( n x )}{n ^{3}}

Streiche

\frac{2 n x cos ( n x )}{n ^{3}} : \frac{2 x cos ( n x )}{n ^{2}}

= \frac{x ^{2} sin ( n x )}{n} - \frac{2 sin ( n x )}{n ^{3}} + \frac{2 x cos ( n x )}{n ^{2}}

s im pl i f y \frac{- 5 z ^{2} - 10 i z + 6}{( z + i ) ^{3}} + 8

e x p an d 80 (e^{- t} - e^{- 2 t})

e x p an d (5 + t + 5 - 5 t, (5 + t)^{2}) \cdot (1, - 1)

e x p an d \frac{( 3 x - 2 ) ^{2}}{9}

e x p an d cos^{2} (x) (sec^{2} (x) + csc^{2} (x))