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人気のある微分積分 >

integral of 1/(x^2+36)

解

\int \frac{1}{x ^{2} + 36} d x

解

\frac{1}{6} arctan (\frac{x}{6}) + C

解答ステップ

\int \frac{1}{x ^{2} + 36} d x

置換積分法を適用する

= \int \frac{1}{6 ( u ^{2} + 1 )} d u

定数を除く:

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

= \frac{1}{6} \cdot \int \frac{1}{u ^{2} + 1} d u

共通積分を使用する:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{6} arctan (u)

代用を戻す

u = \frac{x}{6}

= \frac{1}{6} arctan (\frac{x}{6})

定数を解答に追加する

= \frac{1}{6} arctan (\frac{x}{6}) + C

グラフ

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