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人気のある微分積分 >

integral of (7-1/(x^6))^2(1/(x^7))

解

\int (7 - \frac{1}{x ^{6}})^{2} (\frac{1}{x ^{7}}) d x

解

- \frac{49}{6 x ^{6}} + \frac{7}{6 x ^{12}} - \frac{1}{18 x ^{18}} + C

解答ステップ

\int (7 - \frac{1}{x ^{6}})^{2} \frac{1}{x ^{7}} d x

簡素化

(7 - \frac{1}{x ^{6}})^{2} \frac{1}{x ^{7}} : \frac{( 7 x ^{6} - 1 ) ^{2}}{x ^{19}}

= \int \frac{( 7 x ^{6} - 1 ) ^{2}}{x ^{19}} d x

拡張

\frac{( 7 x ^{6} - 1 ) ^{2}}{x ^{19}} : \frac{49}{x ^{7}} - \frac{14}{x ^{13}} + \frac{1}{x ^{19}}

= \int \frac{49}{x ^{7}} - \frac{14}{x ^{13}} + \frac{1}{x ^{19}} 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 \frac{49}{x ^{7}} d x - \int \frac{14}{x ^{13}} d x + \int \frac{1}{x ^{19}} d x

\int \frac{49}{x ^{7}} d x = - \frac{49}{6 x ^{6}}

\int \frac{14}{x ^{13}} d x = - \frac{7}{6 x ^{12}}

\int \frac{1}{x ^{19}} d x = - \frac{1}{18 x ^{18}}

= - \frac{49}{6 x ^{6}} - (- \frac{7}{6 x ^{12}}) - \frac{1}{18 x ^{18}}

簡素化

= - \frac{49}{6 x ^{6}} + \frac{7}{6 x ^{12}} - \frac{1}{18 x ^{18}}

定数を解答に追加する

= - \frac{49}{6 x ^{6}} + \frac{7}{6 x ^{12}} - \frac{1}{18 x ^{18}} + C

グラフ

人気の例

derivative ln(p)

d er i v a t i v e ln (p)

integral of (3+5x-6x^2-7x^3)/(2x^2)

\int \frac{3 + 5 x - 6 x ^{2} - 7 x ^{3}}{2 x ^{2}} d x

integral of t/(t^4+7)

\int \frac{t}{t ^{4} + 7} d t

勾配 (8-1)(82)

s l o p e (8 - 1) (82)

derivative of 36x

\frac{d}{d x} (36 x)