integral of 16xln(5x)

Lösung

\int 16 x ln (5 x) d x

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

Schritte zur Lösung

\int 16 x ln (5 x) d x

Entferne die Konstante:

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

= 16 \cdot \int x ln (5 x) d x

Wende die partielle Integration an

= 16 (\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x)

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

= 16 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= 16 (\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}) + C

\frac{\partial}{\partial x} (x (x^{2} + y^{2})^{- 1})

f (x) = 4 x cos (x)

d er i v a t i v e x - 9

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