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

Lösung

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

4 (2 e ln (2 e) - 2 e + 1)

Dezimale

19.07335 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 4 [x ln (x) - \int 1 d x]_{1}^{2 e}

\int 1 d x = x

= 4 [x ln (x) - x]_{1}^{2 e}

Berechne die Grenzen:

2 e ln (2 e) - 2 e + 1

= 4 (2 e ln (2 e) - 2 e + 1)

\int_{- 1}^{1} - x^{2} + 2 - x^{2} d x

\int_{0}^{1} \frac{x ^{3}}{2 ( 1 + x ^{4} )} d x

\int_{- 4}^{4} x^{3} - 16 x d x

\int_{1}^{2} x^{3} - x^{2} d x

\int_{- 2}^{1} x + 2 d x