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人気のある微分積分 >

integral from 2 to 7 of 5log_{6}(x)

解

\int_{2}^{7} 5 lo g_{6} (x) d x

解

\frac{5 ( 7 ln ( 7 ) - 5 - 2 ln ( 2 ) )}{ln ( 6 )}

+1

十進法表記

20.18986 \dots

解答ステップ

\int_{2}^{7} 5 lo g_{6} (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_{2}^{7} lo g_{6} (x) d x

部分積分を適用する

= 5 [x lo g_{6} (x) - \int \frac{1}{ln ( 6 )} d x]_{2}^{7}

\int \frac{1}{ln ( 6 )} d x = \frac{1}{ln ( 6 )} x

= 5 [x lo g_{6} (x) - \frac{1}{ln ( 6 )} x]_{2}^{7}

結合

x lo g_{6} (x) - \frac{1}{ln ( 6 )} x : \frac{- x + x ln ( x )}{ln ( 6 )}

= 5 [\frac{- x + x ln ( x )}{ln ( 6 )}]_{2}^{7}

限度を計算する:

\frac{7 ln ( 7 ) - 5 - 2 ln ( 2 )}{ln ( 6 )}

= 5 \cdot \frac{7 ln ( 7 ) - 5 - 2 ln ( 2 )}{ln ( 6 )}

簡素化

= \frac{5 ( 7 ln ( 7 ) - 5 - 2 ln ( 2 ) )}{ln ( 6 )}

グラフ

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