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Beliebt Rechnen >

integral of (ln(x))/((1+x^2)^{1.5)}

Lösung

\int \frac{ln ( x )}{( 1 + x ^{2} ) ^{1.5}} d x

Lösung

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

Schritte zur Lösung

\int \frac{ln ( x )}{( 1 + x ^{2} ) ^{1.5}} d x

Wende die partielle Integration an

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

\int \frac{1}{1 + x ^{2}} d x = ln x^{2} + 1 + x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (ln((e^x)/x))/(x)

\int \frac{ln ( \frac{e ^{x}}{x} )}{x} d x

integral of (e^x*sin(x))

\int (e^{x} \cdot sin (x)) d x

integral of (a^{1/x})/(x^2)

\int \frac{a ^{\frac{1}{x}}}{x ^{2}} d x

integral of (6x^2+3x)/(3x)

\int \frac{6 x ^{2} + 3 x}{3 x} d x

integral of (3x^2)^2

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