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Beliebt Rechnen >

integral of x^2e^{-x^2}

Lösung

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

Lösung

- \frac{1}{2} e^{- x^{2}} x + \frac{π}{4} erf (x) + C

Schritte zur Lösung

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

Vereinfache

x^{2} : xx

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

Wende die partielle Integration an

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

\int - \frac{1}{2} e^{- x^{2}} d x = - \frac{π}{4} erf (x)

= - \frac{1}{2} e^{- x^{2}} x - (- \frac{π}{4} erf (x))

Vereinfache

= - \frac{1}{2} e^{- x^{2}} x + \frac{π}{4} erf (x)

Füge eine Konstante zur Lösung hinzu

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

Beliebte Beispiele

derivative of f(1/3 x^3)=2x^5

\frac{d}{d x} (f (\frac{1}{3} x^{3})) = 2 x^{5}

derivative of 2cos(x+(cos(x))^2)

\frac{d}{d x} (2 cos (x) + (cos (x))^{2})

y^'=(y^4x^4+4x^4)/(y^3)

y^{^{'}} = \frac{y ^{4} x ^{4} + 4 x ^{4}}{y ^{3}}

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\int \frac{x + 7}{x ^{2} ( x + 2 )} d x

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\frac{d}{d x} (\frac{cos ( x ) 2 x ^{3}}{e ^{x}})