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Beliebt Rechnen >

integral of e^{x^{1/2}}

Lösung

\int e^{x^{\frac{1}{2}}} d x

Lösung

2 (e^{x^{\frac{1}{2}}} x^{\frac{1}{2}} - e^{x^{\frac{1}{2}}}) + C

Schritte zur Lösung

\int e^{x^{\frac{1}{2}}} d x

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 = x^{\frac{1}{2}}

ein

= 2 (e^{x^{\frac{1}{2}}} x^{\frac{1}{2}} - e^{x^{\frac{1}{2}}})

Füge eine Konstante zur Lösung hinzu

= 2 (e^{x^{\frac{1}{2}}} x^{\frac{1}{2}} - e^{x^{\frac{1}{2}}}) + C

Graph

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d er i v a t i v e y = (4 x + 3)^{5}

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d er i v a t i v e x^{- \frac{1}{3}}

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d er i v a t i v e f (x) = x - (x + 6)^{6}

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