integral of ln(x)*x^2

Lösung

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

\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9} + C

Schritte zur Lösung

\int ln (x) x^{2} d x

Wende die partielle Integration an

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

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

= \frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9} + C

\int x 5 x^{2} + 1 d x

\int \frac{e ^{- x}}{e ^{- x} + e ^{x}} d x

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

\int \frac{csc ^{2} ( x )}{x} d x

\int \frac{10 x ^{9}}{x ^{10} + 1} d x