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Beliebt Rechnen >

integral of 16xln(7x)

Lösung

\int 16 x ln (7 x) d x

Lösung

16 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}) + C

Schritte zur Lösung

\int 16 x ln (7 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 (7 x) d x

Wende die partielle Integration an

= 16 (\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x)

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

= 16 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= 16 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}) + C

Graph

Beliebte Beispiele

integral from 0 to pi/2 of 11sin^2(2x)

\int_{0}^{\frac{π}{2}} 11 sin^{2} (2 x) d x

derivative of x^3*sin^2(5x)

\frac{d}{d x} (x^{3} \cdot sin^{2} (5 x))

(\partial)/(\partial x)((sin(x))/(sin(y)))

\frac{\partial}{\partial x} (\frac{sin ( x )}{sin ( y )})

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\int 3 x - x^{2} d x

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