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Beliebt Rechnen >

integral of (x+1)*e^{4x+1}

Lösung

\int (x + 1) \cdot e^{4 x + 1} d x

Lösung

e (\frac{1}{4} e^{4 x} x + \frac{3}{16} e^{4 x}) + C

Schritte zur Lösung

\int (x + 1) e^{4 x + 1} d x

(x + 1) e^{4 x + 1} = e^{1} (x + 1) e^{4 x}

= \int e^{1} (x + 1) e^{4 x} d x

Entferne die Konstante:

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

= e^{1} \cdot \int (x + 1) e^{4 x} d x

Vereinfache

= e \cdot \int (x + 1) e^{4 x} d x

Wende die partielle Integration an

= e (\frac{1}{4} e^{4 x} (x + 1) - \int \frac{1}{4} e^{4 x} d x)

\int \frac{1}{4} e^{4 x} d x = \frac{1}{16} e^{4 x}

= e (\frac{1}{4} e^{4 x} (x + 1) - \frac{1}{16} e^{4 x})

Multipliziere aus

\frac{1}{4} e^{4 x} (x + 1) - \frac{1}{16} e^{4 x} : \frac{1}{4} e^{4 x} x + \frac{3}{16} e^{4 x}

= e (\frac{1}{4} e^{4 x} x + \frac{3}{16} e^{4 x})

Füge eine Konstante zur Lösung hinzu

= e (\frac{1}{4} e^{4 x} x + \frac{3}{16} e^{4 x}) + C

Graph

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