integral of (x^2+5)ln(x)

Lösung

\int (x^{2} + 5) ln (x) d x

ln (x) (\frac{x ^{3}}{3} + 5 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 15 x) + C

Schritte zur Lösung

\int (x^{2} + 5) ln (x) d x

Wende die partielle Integration an

= ln (x) (\frac{x ^{3}}{3} + 5 x) - \int \frac{1}{3} (x^{2} + 15) d x

\int \frac{1}{3} (x^{2} + 15) d x = \frac{1}{3} (\frac{x ^{3}}{3} + 15 x)

= ln (x) (\frac{x ^{3}}{3} + 5 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 15 x)

Füge eine Konstante zur Lösung hinzu

= ln (x) (\frac{x ^{3}}{3} + 5 x) - \frac{1}{3} (\frac{x ^{3}}{3} + 15 x) + C

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

\int \frac{- 16}{4 - x ^{2}} d x

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

l a pl a ce t r an s f or m 2 t^{2} - 2 t + 1

d er i v a t i v e f (x) = e^{- x + 1} x - 2 e^{- x + 1}