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Beliebt Rechnen >

integral of xe^{5x+pi}

Lösung

\int x e^{5 x + π} d x

Lösung

\frac{1}{25} (5 e^{5 x + π} x - e^{5 x + π}) + C

Schritte zur Lösung

\int x e^{5 x + π} d x

Wende U-Substitution an

= \int \frac{ln ( u ) - π}{25} d u

Entferne die Konstante:

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

= \frac{1}{25} \cdot \int ln (u) - π d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{25} (\int ln (u) d u - \int π d u)

\int ln (u) d u = u ln (u) - u

\int π d u = π u

= \frac{1}{25} (u ln (u) - u - π u)

Setze in

u = e^{π + 5 x}

ein

= \frac{1}{25} (e^{π + 5 x} ln (e^{π + 5 x}) - e^{π + 5 x} - π e^{π + 5 x})

Vereinfache

\frac{1}{25} (e^{π + 5 x} ln (e^{π + 5 x}) - e^{π + 5 x} - π e^{π + 5 x}) : \frac{1}{25} (5 e^{5 x + π} x - e^{5 x + π})

= \frac{1}{25} (5 e^{5 x + π} x - e^{5 x + π})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{25} (5 e^{5 x + π} x - e^{5 x + π}) + C

Graph

Beliebte Beispiele

limit as x approaches-8 of-(3x)/(x+8)

x \to - 8 lim (- \frac{3 x}{x + 8})

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d er i v a t i v e 3 x^{3} 25 - x^{2}

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\int_{6}^{8} \frac{70}{( x - 6 ) ^{3}} d x

taylor sqrt(1-3x^2)

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f^'(x)=f(x)(1-f(x))

f^{^{'}} (x) = f (x) (1 - f (x))