integral of xln(sqrt(5x))

Lösung

\int x ln (5 x) d x

\frac{1}{2} (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

Schritte zur Lösung

\int x ln (5 x) d x

Vereinfache

x ln (5 x) : \frac{1}{2} x ln (5 x)

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int x ln (5 x) d x

Wende die partielle Integration an

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= \frac{1}{2} (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

\int 2 x + y^{2} d x

a re a y = 10 - (x + 2)^{2}, (- 5.2, 1.2)

\int x + e^{5 x} d x

9 y^{^{''}} + 6 y^{^{'}} + 4 y = 0

\int 2 e^{t} d t