integral from 0 to 1 of 7^{2x}

Lösung

\int_{0}^{1} 7^{2 x} d x

\frac{24}{ln ( 7 )}

Dezimale

12.33356 \dots

Schritte zur Lösung

\int_{0}^{1} 7^{2 x} d x

Vereinfache

7^{2 x} : 4 9^{x}

= \int_{0}^{1} 4 9^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{4 9 ^{x}}{ln ( 49 )}]_{0}^{1}

Vereinfache

ln (49) : 2 ln (7)

= [\frac{4 9 ^{x}}{2 ln ( 7 )}]_{0}^{1}

Berechne die Grenzen:

\frac{24}{ln ( 7 )}

= \frac{24}{ln ( 7 )}

x \to 0 lim (\frac{cos ( 3 x ) tan ( 3 x )}{x})

y^{^{'}} = y - 2 x

\int \frac{4 x ^{3}}{1 + x ^{4}} d x

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

\int_{1}^{8} \frac{5 ln ( x )}{x ^{2}} d x