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人気のある微分積分 >

integral from 1 to e of 1/(xsqrt(ln(x)))

解

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

解

2

解答ステップ

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

u置換積分法を適用する

= \int_{0}^{1} \frac{1}{u} d u

べき乗則を適用する

= [2 u^{\frac{1}{2}}]_{0}^{1}

累乗根の規則を適用する:

a^{\frac{1}{n}} = n a

= [2 u]_{0}^{1}

限度を計算する:

2

= 2

グラフ

人気の例

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

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

integral from-1 to 0 of (e^{1/x})/(x^3)

\int_{- 1}^{0} \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

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

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

integral from 0 to pi/4 of cos(x)-sin(x)

\int_{0}^{\frac{π}{4}} cos (x) - sin (x) d x

integral from 0 to pi/2 of cos(x)sin(x)

\int_{0}^{\frac{π}{2}} cos (x) sin (x) d x