integral from 1 to e of (e^{ln(x)})/x

Lösung

\int_{1}^{e} \frac{e ^{l n (x)}}{x} d x

e - 1

Dezimale

1.71828 \dots

Schritte zur Lösung

\int_{1}^{e} \frac{e ^{l n (x)}}{x} d x

\frac{e ^{l n (x)}}{x} = 1

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

Integral einer Konstanten :

\int a d x = a x

= [1 \cdot x]_{1}^{e}

Vereinfache

= [x]_{1}^{e}

Berechne die Grenzen:

e - 1

= e - 1

\int_{1}^{4} (x + 2 - x^{2}) d x

\int_{- 1}^{0} (x + 1)^{10} x d x

\int_{3}^{7} (8 x + 5) d x

\int_{a}^{7 a} \frac{1}{x} d x

\int_{0}^{u} \frac{t}{t + 1} d t