integral (x-5)ln(x)

Lösung

integral

(x - 5) ln (x)

ln (x) (\frac{x ^{2}}{2} - 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 10 x) + C

Schritte zur Lösung

\int (x - 5) ln (x) d x

Wende die partielle Integration an

= ln (x) (\frac{x ^{2}}{2} - 5 x) - \int \frac{1}{2} (x - 10) d x

\int \frac{1}{2} (x - 10) d x = \frac{1}{2} (\frac{x ^{2}}{2} - 10 x)

= ln (x) (\frac{x ^{2}}{2} - 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 10 x)

Füge eine Konstante zur Lösung hinzu

= ln (x) (\frac{x ^{2}}{2} - 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 10 x) + C

in t e g r a l x^{5} - x + 1

in t e g r a l e^{x} \cdot (\frac{1}{x})

in t e g r a l \frac{1}{( 3 t ^{4} + 4 t ^{2} + 1 )}

in t e g r a l \frac{( x - 2 ) ^{3}}{3 x ^{2}}

in t e g r a l \frac{e ^{3} x}{3}