integral from 1 to e of (8ln(x))

Lösung

\int_{1}^{e} (8 ln (x)) d x

8

Schritte zur Lösung

\int_{1}^{e} 8 ln (x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{1}^{e} ln (x) d x

Wende die partielle Integration an

= 8 [x ln (x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= 8 [x ln (x) - x]_{1}^{e}

Berechne die Grenzen:

1

= 8 \cdot 1

Vereinfache

= 8

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

\int_{1}^{\infty} \frac{1}{x + 6} d x

\int_{11}^{2005} x^{4} - 2 cos (x) d x

\int_{1}^{e} \frac{I n x}{x} d x

\int_{3}^{5} 8 + x^{2} d x