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人気のある微分積分 >

integral from 3 to 9 of 7arctan(x)

解

\int_{3}^{9} 7 arctan (x) d x

解

7 (9 arctan (9) - 3 arctan (3) + \frac{ln ( \frac{5}{41} )}{2})

+1

十進法表記

58.39433 \dots

解答ステップ

\int_{3}^{9} 7 arctan (x) d x

定数を除く:

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

= 7 \cdot \int_{3}^{9} arctan (x) d x

部分積分を適用する

= 7 [x arctan (x) - \int \frac{x}{x ^{2} + 1} d x]_{3}^{9}

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln x^{2} + 1

= 7 [x arctan (x) - \frac{1}{2} ln x^{2} + 1]_{3}^{9}

限度を計算する:

9 arctan (9) - 3 arctan (3) + \frac{- ln ( 82 ) + ln ( 10 )}{2}

= 7 (9 arctan (9) - 3 arctan (3) + \frac{- ln ( 82 ) + ln ( 10 )}{2})

簡素化

= 7 (9 arctan (9) - 3 arctan (3) + \frac{ln ( \frac{5}{41} )}{2})

グラフ

人気の例

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