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人気のある微分積分 >

integral from 1 to e of (4(ln(x))^2+x)/x

解

\int_{1}^{e} \frac{4 ( ln ( x ) ) ^{2} + x}{x} d x

解

e + \frac{1}{3}

+1

十進法表記

3.05161 \dots

解答ステップ

\int_{1}^{e} \frac{4 ( ln ( x ) ) ^{2} + x}{x} d x

簡素化

= \int_{1}^{e} \frac{4 ln ^{2} ( x ) + x}{x} d x

拡張

\frac{4 ln ^{2} ( x ) + x}{x} : \frac{4 ln ^{2} ( x )}{x} + 1

= \int_{1}^{e} \frac{4 ln ^{2} ( x )}{x} + 1 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

= \int_{1}^{e} \frac{4 ln ^{2} ( x )}{x} d x + \int_{1}^{e} 1 d x

\int_{1}^{e} \frac{4 ln ^{2} ( x )}{x} d x = \frac{4}{3}

\int_{1}^{e} 1 d x = e - 1

= \frac{4}{3} + e - 1

分数を組み合わせる

- 1 + \frac{4}{3} : \frac{1}{3}

= e + \frac{1}{3}

グラフ

人気の例

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