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Beliebt Rechnen >

integral of e^{sqrt(t)}

Lösung

\int e^{t} d t

Lösung

2 (e^{t} t - e^{t}) + C

Schritte zur Lösung

\int e^{t} d t

Wende U-Substitution an

= \int e^{u} \cdot 2 u d u

Entferne die Konstante:

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

= 2 \cdot \int e^{u} u d u

Wende die partielle Integration an

= 2 (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

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

Setze in

u = t

ein

= 2 (e^{t} t - e^{t})

Füge eine Konstante zur Lösung hinzu

= 2 (e^{t} t - e^{t}) + C

Graph

Beliebte Beispiele

integral of 3/(sqrt(9-4x^2))

\int \frac{3}{9 - 4 x ^{2}} d x

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\int tan^{3} (x) sec^{11} (x) d x

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\int \frac{x ^{2}}{x ^{3} + 5} d x

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\int x^{- 3} arctan (x) d x

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\int \frac{4}{x ( ln ( x ) ) ^{4}} d x