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Beliebt Rechnen >

integral from 1 to 4 of 2pix(e^x-ln(x))

Lösung

\int_{1}^{4} 2 π x (e^{x} - ln (x)) d x

Lösung

2 π (3 e^{4} - 16 ln (2) + \frac{15}{4})

+1

Dezimale

983.03007 \dots

Schritte zur Lösung

\int_{1}^{4} 2 π x (e^{x} - ln (x)) d x

Entferne die Konstante:

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

= 2 π \cdot \int_{1}^{4} x (e^{x} - ln (x)) d x

Multipliziere aus

x (e^{x} - ln (x)) : e^{x} x - x ln (x)

= 2 π \cdot \int_{1}^{4} e^{x} x - x ln (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 π (\int_{1}^{4} e^{x} x d x - \int_{1}^{4} x ln (x) d x)

\int_{1}^{4} e^{x} x d x = 3 e^{4}

\int_{1}^{4} x ln (x) d x = 16 ln (2) - \frac{15}{4}

= 2 π (3 e^{4} - (16 ln (2) - \frac{15}{4}))

Vereinfache

= 2 π (3 e^{4} - 16 ln (2) + \frac{15}{4})

Graph

Beliebte Beispiele

(4arccos(sqrt(1-x^2)))^'

(4 arccos (1 - x^{2}))^{^{'}}

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\frac{d}{d x} (x^{2} + y^{2} - 9)

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\frac{d}{d x} (sin^{2} (x) - cos (2 x))

limit as x approaches 4+of 5

x \to 4 + lim (5)

integral of sin(ln(14x))

\int sin (ln (14 x)) d x