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Beliebt Rechnen >

integral of 14xln(2x)

Lösung

\int 14 x ln (2 x) d x

Lösung

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

Schritte zur Lösung

\int 14 x ln (2 x) d x

Entferne die Konstante:

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

= 14 \cdot \int x ln (2 x) d x

Wende die partielle Integration an

= 14 (\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x)

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

= 14 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4})

Füge eine Konstante zur Lösung hinzu

= 14 (\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}) + C

Graph

Beliebte Beispiele

derivative of cos^2(3x^7)

\frac{d}{d x} (cos^{2} (3 x^{7}))

(\partial)/(\partial x)(x^{1/4}y^{1/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{1}{4}})

integral of (5^x)/(ln(5))

\int \frac{5 ^{x}}{ln ( 5 )} d x

limit as x approaches infinity of 20

x \to \infty lim (20)

tangent y= 1/(x^2),(-2, 1/4)

t an g e n t y = \frac{1}{x ^{2}}, (- 2, \frac{1}{4})