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人気のある微分積分 >

integral of sqrt(ln(x))

解

\int ln (x) d x

解

x ln (x) - \frac{π}{2} erfi (ln (x)) + C

解答ステップ

\int ln (x) d x

部分積分を適用する

= x ln (x) - \int \frac{1}{2 ln ( x )} d x

\int \frac{1}{2 ln ( x )} d x = \frac{π}{2} erfi (ln (x))

= x ln (x) - \frac{π}{2} erfi (ln (x))

定数を解答に追加する

= x ln (x) - \frac{π}{2} erfi (ln (x)) + C

人気の例

integral of 7x^2+5x-5

\int 7 x^{2} + 5 x - 5 d x

(\partial)/(\partial x)(xsin^2(x))

\frac{\partial}{\partial x} (x sin^{2} (x))

integral of cx^2

\int c x^{2} d x

(\partial)/(\partial u(v))((e^v)/(u(v)+v^2))

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{2}})

integral of (x^2-2)/(x-1)

\int \frac{x ^{2} - 2}{x - 1} d x