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

Lösung

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

8 (x e^{x} - e^{x} + 1)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int 1 d t = t

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

Berechne die Grenzen:

x e^{x} - e^{x} + 1

= 8 (x e^{x} - e^{x} + 1)

\int_{0}^{2} \frac{1}{2} x d x

\int_{1}^{3} (3 x^{2} - 8 x) d x

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\int_{0}^{4} e^{2 x + 1} d x