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Beliebt Rechnen >

integral of y^2e^{y^2}

Lösung

\int y^{2} e^{y^{2}} d y

Lösung

\frac{1}{2} e^{y^{2}} y - \frac{π}{4} erfi (y) + C

Schritte zur Lösung

\int y^{2} e^{y^{2}} d y

Vereinfache

y^{2} : yy

= \int yy e^{y^{2}} d y

Wende die partielle Integration an

= \frac{1}{2} e^{y^{2}} y - \int \frac{1}{2} e^{y^{2}} d y

\int \frac{1}{2} e^{y^{2}} d y = \frac{π}{4} erfi (y)

= \frac{1}{2} e^{y^{2}} y - \frac{π}{4} erfi (y)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} e^{y^{2}} y - \frac{π}{4} erfi (y) + C

Beliebte Beispiele

sum from n=1 to infinity of (1/10)^n

n = 1 \sum \infty (\frac{1}{10})^{n}

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integral of (3x^5-x^3+6)

\int (3 x^{5} - x^{3} + 6) d x