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人気のある微分積分 >

integral of (15)/(25+x^2)

解

\int \frac{15}{25 + x ^{2}} d x

解

3 arctan (\frac{x}{5}) + C

解答ステップ

\int \frac{15}{25 + x ^{2}} d x

定数を除く:

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

= 15 \cdot \int \frac{1}{25 + x ^{2}} d x

置換積分法を適用する

= 15 \cdot \int \frac{1}{5 ( u ^{2} + 1 )} d u

定数を除く:

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

= 15 \cdot \frac{1}{5} \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)

= 15 \cdot \frac{1}{5} arctan (u)

代用を戻す

u = \frac{x}{5}

= 15 \cdot \frac{1}{5} arctan (\frac{x}{5})

簡素化

15 \cdot \frac{1}{5} arctan (\frac{x}{5}) : 3 arctan (\frac{x}{5})

= 3 arctan (\frac{x}{5})

定数を解答に追加する

= 3 arctan (\frac{x}{5}) + C

グラフ

人気の例

limit as x approaches-2 of 2/(x+2)

x \to - 2 lim (\frac{2}{x + 2})

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\int x^{5} (x^{6} - 10)^{4} d x

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