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人気のある微分積分 >

integral of 1/(x(ln(x^4))^6)

解

\int \frac{1}{x ( ln ( x ^{4} ) ) ^{6}} d x

解

- \frac{1}{20480 ln ^{5} ( x )} + C

解答ステップ

\int \frac{1}{x ( ln ( x ^{4} ) ) ^{6}} d x

簡素化

\frac{1}{x ( ln ( x ^{4} ) ) ^{6}} : \frac{1}{4096 x ln ^{6} ( x )}

= \int \frac{1}{4096 x ln ^{6} ( x )} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4096} \cdot \int \frac{1}{x ln ^{6} ( x )} d x

u置換積分法を適用する

= \frac{1}{4096} \cdot \int \frac{1}{u ^{6}} d u

べき乗則を適用する

= \frac{1}{4096} (- \frac{1}{5 u ^{5}})

代用を戻す

u = ln (x)

= \frac{1}{4096} (- \frac{1}{5 ln ^{5} ( x )})

簡素化

\frac{1}{4096} (- \frac{1}{5 ln ^{5} ( x )}) : - \frac{1}{20480 ln ^{5} ( x )}

= - \frac{1}{20480 ln ^{5} ( x )}

定数を解答に追加する

= - \frac{1}{20480 ln ^{5} ( x )} + C

グラフ

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