integral of log_{10}(x+5)

解

\int lo g_{10} (x + 5) d x

x lo g_{10} (x + 5) - \frac{1}{ln ( 10 )} (x + 5 - 5 ln ∣ x + 5 ∣) + C

解答ステップ

\int lo g_{10} (x + 5) d x

部分積分を適用する

= x lo g_{10} (x + 5) - \int \frac{x}{ln ( 10 ) ( x + 5 )} d x

\int \frac{x}{ln ( 10 ) ( x + 5 )} d x = \frac{1}{ln ( 10 )} (x + 5 - 5 ln ∣ x + 5 ∣)

= x lo g_{10} (x + 5) - \frac{1}{ln ( 10 )} (x + 5 - 5 ln ∣ x + 5 ∣)

定数を解答に追加する

= x lo g_{10} (x + 5) - \frac{1}{ln ( 10 )} (x + 5 - 5 ln ∣ x + 5 ∣) + C