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人気のある微分積分 >

integral of 5/(3-2cos(x))

解

\int \frac{5}{3 - 2 cos ( x )} d x

解

25 arctan (5 tan (\frac{x}{2})) + C

解答ステップ

\int \frac{5}{3 - 2 cos ( x )} d x

定数を除く:

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

= 5 \cdot \int \frac{1}{3 - 2 cos ( x )} d x

u置換積分法を適用する

= 5 \cdot \int \frac{2}{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

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

置換積分法を適用する

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

定数を除く:

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

= 5 \cdot 2 \cdot \frac{1}{5} \cdot \int \frac{1}{v ^{2} + 1} d v

共通積分を使用する:

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

= 5 \cdot 2 \cdot \frac{1}{5} arctan (v)

代用を戻す

= 5 \cdot 2 \cdot \frac{1}{5} arctan (5 tan (\frac{x}{2}))

簡素化

5 \cdot 2 \cdot \frac{1}{5} arctan (5 tan (\frac{x}{2})) : 25 arctan (5 tan (\frac{x}{2}))

= 25 arctan (5 tan (\frac{x}{2}))

定数を解答に追加する

= 25 arctan (5 tan (\frac{x}{2})) + C

グラフ

人気の例

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