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人気のある微分積分 >

integral from a to a+b of 1/x

解

\int_{a}^{a + b} \frac{1}{x} d x

解

ln ∣ a + b ∣ - ln ∣ a ∣

解答ステップ

\int_{a}^{a + b} \frac{1}{x} d x

共通積分を使用する:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{a}^{a + b}

限度を計算する:

ln ∣ a + b ∣ - ln ∣ a ∣

= ln ∣ a + b ∣ - ln ∣ a ∣

人気の例

integral from 1 to e of (((ln(x))^5))/x

\int_{1}^{e} \frac{( ( ln ( x ) ) ^{5} )}{x} d x

integral from 2y to 3-y of (x+y)

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

integral from 1 to 5 of (3+2/x)

\int_{1}^{5} (3 + \frac{2}{x}) d x

integral from 0 to 2 of r^3sqrt(4-r^2)

\int_{0}^{2} r^{3} 4 - r^{2} d r

integral from-pi to pi of sin(4x)

\int_{- π}^{π} sin (4 x) d x