integral of ln(x)*x

Lösung

\int ln (x) \cdot x d x

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

Schritte zur Lösung

\int ln (x) x d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

t an g e n t f (x) = 2 x 3 - 4 x, at x = - 1

\int - 5 x^{- 1} d x

\int_{- \infty}^{4} \frac{1}{x ^{2} + 1} d x

s im pl i f y (\frac{3 x ^{2} - 2}{2 x + 3})^{3}

\int (5 x^{2} + 6 x - 8) d x