integral from 0 to (ln(6))/4 of ((5e^{4u}))/(sqrt(e^{4u)+3)}

Lösung

\int_{0}^{\frac{l n ( 6 )}{4}} \frac{( 5 e ^{4 u} )}{e ^{4 u} + 3} d u

\frac{5}{2}

Dezimale

2.5

Schritte zur Lösung

\int_{0}^{\frac{l n ( 6 )}{4}} \frac{5 e ^{4 u}}{e ^{4 u} + 3} d u

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{\frac{l n ( 6 )}{4}} \frac{e ^{4 u}}{e ^{4 u} + 3} d u

Wende U-Substitution an

= 5 \cdot \int_{4}^{9} \frac{1}{4 v} d v

Entferne die Konstante:

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

= 5 \cdot \frac{1}{4} \cdot \int_{4}^{9} \frac{1}{v} d v

Wende die Potenzregel an

= 5 \cdot \frac{1}{4} [2 v^{\frac{1}{2}}]_{4}^{9}

Vereinfache

5 \cdot \frac{1}{4} [2 v^{\frac{1}{2}}]_{4}^{9} : \frac{5}{4} [2 v]_{4}^{9}

= \frac{5}{4} [2 v]_{4}^{9}

Berechne die Grenzen:

2

= \frac{5}{4} \cdot 2

Vereinfache

= \frac{5}{2}

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