integral of (e^{x^2})/(x^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{2 x - 1}{x ^{2} + x} d x

\int \frac{x}{1 - 4 x - x ^{2}} d x

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

\int \frac{1}{( x + 1 ) ^{2} ( x + 2 )} d x

\int \frac{1}{8 x - 3} d x