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Beliebt Rechnen >

integral from 3 to 12 of ln(x^8)

Lösung

\int_{3}^{12} ln (x^{8}) d x

Lösung

24 ln (6912) - 72

+1

Dezimale

140.18434 \dots

Schritte zur Lösung

\int_{3}^{12} ln (x^{8}) d x

Wende die partielle Integration an

= [x ln (x^{8}) - \int 8 d x]_{3}^{12}

\int 8 d x = 8 x

= [x ln (x^{8}) - 8 x]_{3}^{12}

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= [8 x ln (x) - 8 x]_{3}^{12}

Berechne die Grenzen:

96 ln (12) - 72 - 24 ln (3)

= 96 ln (12) - 72 - 24 ln (3)

Vereinfache

= 24 ln (6912) - 72

Graph

Beliebte Beispiele

y^{^{'}} = - \frac{1}{2} y

integral of ((12)/x+x/(12))

\int (\frac{12}{x} + \frac{x}{12}) d x

xy^'+3y=(2e^{4x})/(x^2)

x y^{^{'}} + 3 y = \frac{2 e ^{4 x}}{x ^{2}}

derivative of ax^2e^{-x}

\frac{d}{d x} (a x^{2} e^{- x})

derivative of ln(3/(x^2+9))

\frac{d}{d x} (ln (\frac{3}{x ^{2} + 9}))