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人気のある微分積分 >

integral from 4 to 6 of x(1/(x-3))

解

\int_{4}^{6} x (\frac{1}{x - 3}) d x

解

2 + 3 ln (3)

+1

十進法表記

5.29583 \dots

解答ステップ

\int_{4}^{6} x \frac{1}{x - 3} d x

簡素化

x \frac{1}{x - 3} : \frac{x}{x - 3}

= \int_{4}^{6} \frac{x}{x - 3} d x

u置換積分法を適用する

= \int_{1}^{3} \frac{u + 3}{u} d u

拡張

\frac{u + 3}{u} : 1 + \frac{3}{u}

= \int_{1}^{3} 1 + \frac{3}{u} d u

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}^{3} 1 d u + \int_{1}^{3} \frac{3}{u} d u

\int_{1}^{3} 1 d u = 2

\int_{1}^{3} \frac{3}{u} d u = 3 ln (3)

= 2 + 3 ln (3)

グラフ

人気の例

integral from 1 to 4 of (x^3-3x^2+1)

\int_{1}^{4} (x^{3} - 3 x^{2} + 1) d x

integral from 0 to-1 of x*e^x

\int_{0}^{- 1} x \cdot e^{x} d x

integral from 0 to 2 of sqrt((x+2)^2-3)

\int_{0}^{2} (x + 2)^{2} - 3 d x

integral from 5 to 10 of 1

\int_{5}^{10} 1

integral from-2 to 0 of (-2x)/(1+x^2)

\int_{- 2}^{0} \frac{- 2 x}{1 + x ^{2}} d x