integral of (18x+4)(9x^2+4x)^5

解

\int (18 x + 4) (9 x^{2} + 4 x)^{5} d x

\frac{177147 x ^{12}}{2} + 236196 x^{11} + 262440 x^{10} + 155520 x^{9} + 51840 x^{8} + 9216 x^{7} + \frac{2048 x ^{6}}{3} + C

解答ステップ

\int (18 x + 4) (9 x^{2} + 4 x)^{5} d x

拡張

(18 x + 4) (9 x^{2} + 4 x)^{5} : 1062882 x^{11} + 2598156 x^{10} + 2624400 x^{9} + 1399680 x^{8} + 414720 x^{7} + 64512 x^{6} + 4096 x^{5}

= \int 1062882 x^{11} + 2598156 x^{10} + 2624400 x^{9} + 1399680 x^{8} + 414720 x^{7} + 64512 x^{6} + 4096 x^{5} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1062882 x^{11} d x + \int 2598156 x^{10} d x + \int 2624400 x^{9} d x + \int 1399680 x^{8} d x + \int 414720 x^{7} d x + \int 64512 x^{6} d x + \int 4096 x^{5} d x

\int 1062882 x^{11} d x = \frac{177147 x ^{12}}{2}

\int 2598156 x^{10} d x = 236196 x^{11}

\int 2624400 x^{9} d x = 262440 x^{10}

\int 1399680 x^{8} d x = 155520 x^{9}

\int 414720 x^{7} d x = 51840 x^{8}

\int 64512 x^{6} d x = 9216 x^{7}

\int 4096 x^{5} d x = \frac{2048 x ^{6}}{3}

= \frac{177147 x ^{12}}{2} + 236196 x^{11} + 262440 x^{10} + 155520 x^{9} + 51840 x^{8} + 9216 x^{7} + \frac{2048 x ^{6}}{3}

定数を解答に追加する

= \frac{177147 x ^{12}}{2} + 236196 x^{11} + 262440 x^{10} + 155520 x^{9} + 51840 x^{8} + 9216 x^{7} + \frac{2048 x ^{6}}{3} + C