展开 (-x^2cos(x)+2(xsin(x)+cos(x))+C)/x

解答

展开

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

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

求解步骤

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

乘开

- 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}

使用分式法则:

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

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

消掉

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

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

消掉

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

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

e x p an d \frac{1}{3} e^{3 x} (x - \frac{1}{3})

e x p an d (e^{4 t} + e^{- 4 t})^{2}

e x p an d \frac{( x ^{3} + 5 x ^{2} + 9 x + 7 )}{( ( x + 1 ) ( x + 2 ) )}

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

e x p an d \frac{8 ( 2 s + 24 )}{s ^{3} - 4 s ^{2} + 30 s + 333}