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人気のある微分積分 >

integral of 7/(x(ln(x))^2)

解

\int \frac{7}{x ( ln ( x ) ) ^{2}} d x

解

- \frac{7}{ln ( x )} + C

解答ステップ

\int \frac{7}{x ( ln ( x ) ) ^{2}} d x

定数を除く:

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

= 7 \cdot \int \frac{1}{x ( ln ( x ) ) ^{2}} d x

u置換積分法を適用する

= 7 \cdot \int \frac{1}{u ^{2}} d u

べき乗則を適用する

= 7 (- \frac{1}{u})

代用を戻す

u = ln (x)

= 7 (- \frac{1}{ln ( x )})

簡素化

7 (- \frac{1}{ln ( x )}) : - \frac{7}{ln ( x )}

= - \frac{7}{ln ( x )}

定数を解答に追加する

= - \frac{7}{ln ( x )} + C

グラフ

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