integral of 3/x+e*e^{-x}-x^{-3/2}

Lösung

\int \frac{3}{x} + e \cdot e^{- x} - x^{- \frac{3}{2}} d x

3 ln ∣ x ∣ - e^{1 - x} + \frac{2}{x ^{\frac{1}{2}}} + C

Schritte zur Lösung

\int \frac{3}{x} + e e^{- x} - x^{- \frac{3}{2}} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{3}{x} d x + \int e e^{- x} d x - \int x^{- \frac{3}{2}} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int e e^{- x} d x = - e^{1 - x}

\int x^{- \frac{3}{2}} d x = - \frac{2}{x ^{\frac{1}{2}}}

= 3 ln ∣ x ∣ - e^{1 - x} - (- \frac{2}{x ^{\frac{1}{2}}})

Vereinfache

= 3 ln ∣ x ∣ - e^{1 - x} + \frac{2}{x ^{\frac{1}{2}}}

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x ∣ - e^{1 - x} + \frac{2}{x ^{\frac{1}{2}}} + C

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