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Beliebt Rechnen >

integral from 0 to 1 of xe^{3x^2}

Lösung

\int_{0}^{1} x e^{3 x^{2}} d x

Lösung

\frac{e ^{3} - 1}{6}

+1

Dezimale

3.18092 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{3 x^{2}} d x

Wende U-Substitution an

= \int_{0}^{3} \frac{e ^{u}}{6} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{0}^{3} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= \frac{1}{6} [e^{u}]_{0}^{3}

Berechne die Grenzen:

e^{3} - 1

= \frac{1}{6} (e^{3} - 1)

Vereinfache

= \frac{e ^{3} - 1}{6}

Graph

Beliebte Beispiele

integral of (x^3)/(x-2)

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

derivative of ln(x^4+1)

\frac{d}{d x} (ln (x^{4} + 1))

y^{''}+10y^'+25y=5e^{-5t}

y^{^{''}} + 10 y^{^{'}} + 25 y = 5 e^{- 5 t}

(d^2)/(dx^2)(2/(3x^4))

\frac{d ^{2}}{d x ^{2}} (\frac{2}{3 x ^{4}})

integral of+7xcos(4x)

\int + 7 x cos (4 x) d x