integral of x^{-1/2}*ln(x)

Lösung

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

2 x^{\frac{1}{2}} ln (x) - 4 x^{\frac{1}{2}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{2}{x ^{\frac{1}{2}}} d x = 4 x^{\frac{1}{2}}

= 2 x^{\frac{1}{2}} ln (x) - 4 x^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 x^{\frac{1}{2}} ln (x) - 4 x^{\frac{1}{2}} + C

x \to \frac{π}{4} lim (sec (x) tan (x))

x \to 0 + lim (ln (sin (x)))

\frac{d}{d x} (- x^{3} + 4)

\frac{\partial}{\partial x} (\frac{y}{2 x} - 1)

\int e^{- x} tan (e^{- x}) d x