integral of sqrt(x)*ln(x)

Lösung

\int x \cdot ln (x) d x

\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}} + C

Schritte zur Lösung

\int x ln (x) d x

Wende die partielle Integration an

= \frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= \frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}} + C

\int_{- 4}^{0} (1 + 16 - x^{2}) d x

\int t^{2} 13 t - 1 d t

d er i v a t i v e f (x) = (\frac{4}{x}) + (\frac{1}{5 x ^{3} + 2 x})

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

x y^{^{'}} - 2 y = 0