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人気のある微分積分 >

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

解

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

解

- \frac{5}{2} x + ln ∣ x ∣ + C

解答ステップ

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

定数を除く:

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

= \frac{1}{- 2} \cdot \int \frac{5 x - 2}{x} d x

簡素化

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

拡張

\frac{5 x - 2}{x} : 5 - \frac{2}{x}

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 5 d x = 5 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= (- \frac{1}{2}) (5 x - 2 ln ∣ x ∣)

簡素化

(- \frac{1}{2}) (5 x - 2 ln ∣ x ∣) : - \frac{5}{2} x + ln ∣ x ∣

= - \frac{5}{2} x + ln ∣ x ∣

定数を解答に追加する

= - \frac{5}{2} x + ln ∣ x ∣ + C

グラフ

人気の例

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

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

integral of (6x^2-11x+7)/(3x-1)

\int \frac{6 x ^{2} - 11 x + 7}{3 x - 1} d x

integral of (1x-2)/(sqrt(x)+4)

\int \frac{1 x - 2}{x + 4} d x

integral of 2xtan^2(x^2)

\int 2 x tan^{2} (x^{2}) d x

integral of (e^x-x)^2

\int (e^{x} - x)^{2} d x