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人気のある微分積分 >

integral of (2x+3sqrt(x))/(4x^2)

解

\int \frac{2 x + 3 x}{4 x ^{2}} d x

解

\frac{1}{4} (2 ln ∣ x ∣ - \frac{6}{x}) + C

解答ステップ

\int \frac{2 x + 3 x}{4 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}{4} \cdot \int \frac{2 x + 3 x}{x ^{2}} d x

簡素化

\frac{2 x + 3 x}{x ^{2}} : \frac{2 x + 3}{x ^{\frac{3}{2}}}

= \frac{1}{4} \cdot \int \frac{2 x + 3}{x ^{\frac{3}{2}}} d x

拡張

\frac{2 x + 3}{x ^{\frac{3}{2}}} : \frac{2}{x} + \frac{3}{x ^{\frac{3}{2}}}

= \frac{1}{4} \cdot \int \frac{2}{x} + \frac{3}{x ^{\frac{3}{2}}} 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}{4} (\int \frac{2}{x} d x + \int \frac{3}{x ^{\frac{3}{2}}} d x)

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{3}{x ^{\frac{3}{2}}} d x = - \frac{6}{x}

= \frac{1}{4} (2 ln ∣ x ∣ - \frac{6}{x})

定数を解答に追加する

= \frac{1}{4} (2 ln ∣ x ∣ - \frac{6}{x}) + C

グラフ

人気の例

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\int cos^{6} (y) sin^{3} (y) d y

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\int \frac{\frac{1}{x}}{x ^{4}} d x

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\int \frac{1}{x ^{2} ( a ^{2} - x ^{2} ) ^{\frac{1}{2}}} d x

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\int e^{- x} sin (π x) d x

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

\int \frac{x - 3}{x ^{2} + 3 x + 3} d x