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人気のある微分積分 >

integral from y to e of (ln(x))/x

解

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

解

\frac{1 - ln ^{2} ( y )}{2}

解答ステップ

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

u置換積分法を適用する

= \int_{l n (y)}^{1} u d u

べき乗則を適用する

= [\frac{u ^{2}}{2}]_{l n (y)}^{1}

限度を計算する:

\frac{1}{2} - \frac{ln ^{2} ( y )}{2}

= \frac{1}{2} - \frac{ln ^{2} ( y )}{2}

簡素化

= \frac{1 - ln ^{2} ( y )}{2}

人気の例

integral from 4 to infinity of 1/(x^4)

\int_{4}^{\infty} \frac{1}{x ^{4}} d x

integral from 0 to 2 of 2t(sqrt(t^2+1))

\int_{0}^{2} 2 t (t^{2} + 1) d t

integral from 0 to 1/2 of t

\int_{0}^{\frac{1}{2}} t d t

integral from-infinity to 0 of e^{2t}

\int_{- \infty}^{0} e^{2 t} d t

integral from 0 to a of cosh(t/a)

\int_{0}^{a} cosh (\frac{t}{a}) d t