erweitern (-x^2cos(x)+2(xsin(x)+cos(x))+C)/(x^2)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

Streiche

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

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

e x p an d x (3 + 2 ln (x)) d x

e x p an d (1, 2, - 5) x (2, 3, 1)

e x p an d \frac{( x ^{2} + 2 x - 5 )}{x ( x ^{2} - 4 )}

e x p an d 7 (p - 3 = 35)

s im pl i f y (c - q) (c + q)