integral from 0 to 1 of-8x5^x

Lösung

\int_{0}^{1} - 8 x 5^{x} d x

- \frac{8 ( 5 ln ( 5 ) - 4 )}{ln ^{2} ( 5 )}

Dezimale

- 12.49957 \dots

Schritte zur Lösung

\int_{0}^{1} - 8 x \cdot 5^{x} d x

Entferne die Konstante:

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

= - 8 \cdot \int_{0}^{1} x \cdot 5^{x} d x

Wende die partielle Integration an

= - 8 [\frac{5 ^{x} x}{ln ( 5 )} - \int \frac{5 ^{x}}{ln ( 5 )} d x]_{0}^{1}

\int \frac{5 ^{x}}{ln ( 5 )} d x = \frac{5 ^{x}}{ln ^{2} ( 5 )}

= - 8 [\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}]_{0}^{1}

Berechne die Grenzen:

\frac{5 ln ( 5 ) - 4}{ln ^{2} ( 5 )}

= - 8 \cdot \frac{5 ln ( 5 ) - 4}{ln ^{2} ( 5 )}

Vereinfache

= - \frac{8 ( 5 ln ( 5 ) - 4 )}{ln ^{2} ( 5 )}

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

\int cos^{8} (θ) sin (θ) d θ

s l o p e y - 3 = 5 (x - 2) y - 3 = 5 (x - 2)

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

\frac{\partial}{\partial y} (\frac{y}{x ^{2} - y ^{2}})