integral of (e^x)/(x^2)*e^x+2x

Lösung

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

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

Schritte zur Lösung

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

\int \frac{e ^{x}}{x ^{2}} e^{x} d x = - \frac{e ^{2 x}}{x} + 2 Ei (2 x)

\int 2 x d x = x^{2}

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

Füge eine Konstante zur Lösung hinzu

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

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