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Beliebt Rechnen >

integral of xln(2x^2+1)

Lösung

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

Lösung

\frac{1}{2} x^{2} ln (2 x^{2} + 1) - 2 (\frac{x ^{2}}{4} - \frac{1}{8} ln 2 x^{2} + 1) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{2 x ^{3}}{2 x ^{2} + 1} d x = 2 (\frac{x ^{2}}{4} - \frac{1}{8} ln 2 x^{2} + 1)

= \frac{1}{2} x^{2} ln (2 x^{2} + 1) - 2 (\frac{x ^{2}}{4} - \frac{1}{8} ln 2 x^{2} + 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} ln (2 x^{2} + 1) - 2 (\frac{x ^{2}}{4} - \frac{1}{8} ln 2 x^{2} + 1) + C

Graph

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