integral from 0 to 1 of (5^x)/(5^x+1)

Lösung

\int_{0}^{1} \frac{5 ^{x}}{5 ^{x} + 1} d x

\frac{ln ( 3 )}{ln ( 5 )}

Dezimale

0.68260 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{5 ^{x}}{5 ^{x} + 1} d x

Wende U-Substitution an

= \int_{2}^{6} \frac{1}{ln ( 5 ) u} d u

Entferne die Konstante:

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

= \frac{1}{ln ( 5 )} \cdot \int_{2}^{6} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{ln ( 5 )} [ln ∣ u ∣]_{2}^{6}

Berechne die Grenzen:

ln (6) - ln (2)

= \frac{1}{ln ( 5 )} (ln (6) - ln (2))

Vereinfache

= \frac{ln ( 3 )}{ln ( 5 )}

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

\int_{0}^{1} c x^{2} (1 - x) d x

\int_{0}^{8} 8 e^{- 8 x} d x

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

\int_{0}^{\infty} \frac{4}{x ^{2}} d x