integral from 0 to 1 of 4e^{6sqrt(x)}

Lösung

\int_{0}^{1} 4 e^{6 x} d x

\frac{2 ( 5 e ^{6} + 1 )}{9}

Dezimale

448.47643 \dots

Schritte zur Lösung

\int_{0}^{1} 4 e^{6 x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{0}^{1} e^{6 x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{6} \frac{e ^{u} u}{18} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{18} \cdot \int_{0}^{6} e^{u} u d u

Wende die partielle Integration an

= 4 \cdot \frac{1}{18} [e^{u} u - \int e^{u} d u]_{0}^{6}

\int e^{u} d u = e^{u}

= 4 \cdot \frac{1}{18} [e^{u} u - e^{u}]_{0}^{6}

Vereinfache

4 \cdot \frac{1}{18} [e^{u} u - e^{u}]_{0}^{6} : \frac{2}{9} [e^{u} u - e^{u}]_{0}^{6}

= \frac{2}{9} [e^{u} u - e^{u}]_{0}^{6}

Berechne die Grenzen:

5 e^{6} + 1

= \frac{2}{9} (5 e^{6} + 1)

Vereinfache

= \frac{2 ( 5 e ^{6} + 1 )}{9}

n = 0 \sum \infty \frac{3 ^{n}}{n !}

\frac{d}{d x} ((x) cos (x) sin (x))

\frac{\partial}{\partial x} (e^{2 (2 x + y)})

d er i v a t i v e ln (x^{2} - 1)

n = 0 \sum \infty n x^{n - 1}