integral from x to a of 2^{ln(t)}

Lösung

\int_{x}^{a} 2^{l n (t)} d t

\frac{( 2 e ) ^{l n (a)} - ( 2 e ) ^{l n (x)}}{ln ( 2 e )}

Schritte zur Lösung

\int_{x}^{a} 2^{l n (t)} d t

Wende U-Substitution an

= \int_{l n (x)}^{l n (a)} 2^{u} e^{u} d u

Wende Exponentenregel an:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

2^{u} e^{u} = (2 e)^{u}

= \int_{l n (x)}^{l n (a)} (2 e)^{u} d u

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

= [\frac{( 2 e ) ^{u}}{ln ( 2 e )}]_{l n (x)}^{l n (a)}

Berechne die Grenzen:

\frac{( 2 e ) ^{l n (a)}}{ln ( 2 e )} - \frac{( 2 e ) ^{l n (x)}}{ln ( 2 e )}

= \frac{( 2 e ) ^{l n (a)}}{ln ( 2 e )} - \frac{( 2 e ) ^{l n (x)}}{ln ( 2 e )}

Vereinfache

= \frac{( 2 e ) ^{l n (a)} - ( 2 e ) ^{l n (x)}}{ln ( 2 e )}

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