展開する 10(2+xsin(3x))^9*sin(3x)+3xcos(3x)

解

展開する

10 (2 + x sin (3 x))^{9} \cdot sin (3 x) + 3 x cos (3 x)

5120 sin (3 x) + 23040 x sin^{2} (3 x) + 46080 sin^{3} (3 x) x^{2} + 53760 sin^{4} (3 x) x^{3} + 40320 sin^{5} (3 x) x^{4} + 20160 sin^{6} (3 x) x^{5} + 6720 sin^{7} (3 x) x^{6} + 1440 sin^{8} (3 x) x^{7} + 180 sin^{9} (3 x) x^{8} + 10 sin^{10} (3 x) x^{9} + 3 x cos (3 x)

解答ステップ

10 (2 + x sin (3 x))^{9} sin (3 x) + 3 x cos (3 x)

= 10 sin (3 x) (2 + x sin (3 x))^{9} + 3 x cos (3 x)

拡張

10 sin (3 x) (2 + x sin (3 x))^{9} : 5120 sin (3 x) + 23040 x sin^{2} (3 x) + 46080 sin^{3} (3 x) x^{2} + 53760 sin^{4} (3 x) x^{3} + 40320 sin^{5} (3 x) x^{4} + 20160 sin^{6} (3 x) x^{5} + 6720 sin^{7} (3 x) x^{6} + 1440 sin^{8} (3 x) x^{7} + 180 sin^{9} (3 x) x^{8} + 10 sin^{10} (3 x) x^{9}

= 5120 sin (3 x) + 23040 x sin^{2} (3 x) + 46080 sin^{3} (3 x) x^{2} + 53760 sin^{4} (3 x) x^{3} + 40320 sin^{5} (3 x) x^{4} + 20160 sin^{6} (3 x) x^{5} + 6720 sin^{7} (3 x) x^{6} + 1440 sin^{8} (3 x) x^{7} + 180 sin^{9} (3 x) x^{8} + 10 sin^{10} (3 x) x^{9} + 3 x cos (3 x)