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人気のある微分積分 >

integral from 1 to t of (ln(x))/x

解

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

解

\frac{ln ^{2} ( t )}{2}

解答ステップ

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

u置換積分法を適用する

= \int_{0}^{l n (t)} u d u

べき乗則を適用する

= [\frac{u ^{2}}{2}]_{0}^{l n (t)}

限度を計算する:

\frac{ln ^{2} ( t )}{2}

= \frac{ln ^{2} ( t )}{2}

人気の例

integral from l to u of r*e^{-t*r}

\int_{l}^{u} r \cdot e^{- t \cdot r} d t

integral from 4 to 5.2 of ln(x)

\int_{4}^{5.2} ln (x) d x

integral from 2 to 3.8 of ln(5-x)

\int_{2}^{3.8} ln (5 - x) d x

integral from 0 to 4 of 1/(16+t^2)

\int_{0}^{4} \frac{1}{16 + t ^{2}} d t

integral from 0 to 2*pi of sin^2(x)

\int_{0}^{2 \cdot π} sin^{2} (x) d x