integral of sqrt(2)xln(4x)

Lösung

\int 2 \cdot x \cdot ln (4 x) d x

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

Schritte zur Lösung

\int 2 x ln (4 x) d x

Entferne die Konstante:

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

= 2 \cdot \int x ln (4 x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int y x d x

\int_{0}^{π} sin^{2} (t co) s^{4} t d t

\frac{d y}{d t} = 0.225 - \frac{y}{200}, y (0) = 90

t a y l or (x^{2} + 1) \cdot e^{x - 1}

im pl i c i t \frac{d y}{d x}, y = x^{\frac{15}{16}}