integral of xln(3x^2)

Lösung

\int x ln (3 x^{2}) d x

\frac{1}{2} ln (3) x^{2} + x^{2} ln (x) - \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int x ln (3 x^{2}) d x

Wende die partielle Integration an

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

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

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

Vereinfache

\frac{1}{2} x^{2} ln (3 x^{2}) - \frac{x ^{2}}{2} : \frac{1}{2} ln (3) x^{2} + x^{2} ln (x) - \frac{x ^{2}}{2}

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln (3) x^{2} + x^{2} ln (x) - \frac{x ^{2}}{2} + C

\frac{1}{x} d x + d y = 0

d er i v a t i v e arctan (e^{4 x})

d er i v a t i v e - \frac{5}{3 x}

d er i v a t i v e arccos (4 x^{9})

d er i v a t i v e y = \frac{x ^{3}}{1 - x ^{2}}