展开-1/5 (2x^2+x-12)^5+C

解答

展开

- \frac{1}{5} (2 x^{2} + x - 12)^{5} + C

- \frac{32 x ^{10}}{5} - \frac{16801 x ^{5}}{5} + \frac{248832}{5} - 16 x^{9} + 176 x^{8} + 376 x^{7} - 2018 x^{6} + 12108 x^{4} + 13536 x^{3} - 38016 x^{2} - 20736 x + C

求解步骤

- \frac{1}{5} (2 x^{2} + x - 12)^{5} + C

(2 x^{2} + x - 12)^{5} = 32 x^{10} + 80 x^{9} - 880 x^{8} - 1880 x^{7} + 10090 x^{6} + 16801 x^{5} - 60540 x^{4} - 67680 x^{3} + 190080 x^{2} + 103680 x - 248832

= - \frac{1}{5} (32 x^{10} + 80 x^{9} - 880 x^{8} - 1880 x^{7} + 10090 x^{6} + 16801 x^{5} - 60540 x^{4} - 67680 x^{3} + 190080 x^{2} + 103680 x - 248832) + C

乘开

- \frac{1}{5} (32 x^{10} + 80 x^{9} - 880 x^{8} - 1880 x^{7} + 10090 x^{6} + 16801 x^{5} - 60540 x^{4} - 67680 x^{3} + 190080 x^{2} + 103680 x - 248832) : \frac{- 32 x ^{10} - 16801 x ^{5} + 248832}{5} - 16 x^{9} + 176 x^{8} + 376 x^{7} - 2018 x^{6} + 12108 x^{4} + 13536 x^{3} - 38016 x^{2} - 20736 x

= \frac{- 32 x ^{10} - 16801 x ^{5} + 248832}{5} - 16 x^{9} + 176 x^{8} + 376 x^{7} - 2018 x^{6} + 12108 x^{4} + 13536 x^{3} - 38016 x^{2} - 20736 x + C

使用分式法则:

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

\frac{- 32 x ^{10} - 16801 x ^{5} + 248832}{5} = - \frac{32 x ^{10}}{5} - \frac{16801 x ^{5}}{5} + \frac{248832}{5}

= - \frac{32 x ^{10}}{5} - \frac{16801 x ^{5}}{5} + \frac{248832}{5} - 16 x^{9} + 176 x^{8} + 376 x^{7} - 2018 x^{6} + 12108 x^{4} + 13536 x^{3} - 38016 x^{2} - 20736 x + C

e x p an d \frac{( 4 x ^{4} + 9 x ^{3} + 42 x ^{2} + 51 x + 36 )}{3 x ( x ^{2} + 6 ) ^{2}}

\frac{d}{d t} ((x) (x - 1) (1 - 2 x))

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

s im pl i f y (\frac{197}{193} - 0.25 (\frac{394}{193})) \cdot 1 0^{3}

e x p an d \frac{( 6 x + 54 ) ( 2 x + 18 )}{( 25 x + 35 ) ( 5 x + 7 )}