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Beliebt Rechnen >

integral from b to 1 of 3ln(x)

Lösung

\int_{b}^{1} 3 ln (x) d x

Lösung

3 (- 1 - b ln (b) + b)

Schritte zur Lösung

\int_{b}^{1} 3 ln (x) d x

Entferne die Konstante:

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

= 3 \cdot \int_{b}^{1} ln (x) d x

Wende die partielle Integration an

= 3 [x ln (x) - \int 1 d x]_{b}^{1}

\int 1 d x = x

= 3 [x ln (x) - x]_{b}^{1}

Berechne die Grenzen:

- 1 - b ln (b) + b

= 3 (- 1 - b ln (b) + b)

Beliebte Beispiele

integral of 5x 3/2

\int 5 x \frac{3}{2} d x

derivative of (e^{-x}/x)

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

integral from-1 to 1 of e^y-(y^2-9)

\int_{- 1}^{1} e^{y} - (y^{2} - 9) d y

(14-6y+e-3x)dx-2dy=0

(14 - 6 y + e - 3 x) d x - 2 d y = 0

integral from 0 to 6 of pi/8 (6-x)^2

\int_{0}^{6} \frac{π}{8} (6 - x)^{2} d x