integral of xe^{10x}

Lösung

\int x e^{10 x} d x

\frac{1}{100} (e^{10 x} \cdot 10 x - e^{10 x}) + C

Schritte zur Lösung

\int x e^{10 x} d x

Wende U-Substitution an

= \int \frac{e ^{u} u}{100} d u

Entferne die Konstante:

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

= \frac{1}{100} \cdot \int e^{u} u d u

Wende die partielle Integration an

= \frac{1}{100} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{100} (e^{u} u - e^{u})

Setze in

u = 10 x

ein

= \frac{1}{100} (e^{10 x} \cdot 10 x - e^{10 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{100} (e^{10 x} \cdot 10 x - e^{10 x}) + C

x \to - b lim \frac{( ( x + b ) ^{7} + ( x + b ) ^{10} )}{4 ( x + b )}

\frac{\partial}{\partial x} ((x + y)^{2} + (x + 1)^{2})

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

\frac{\partial}{\partial x} (x + y^{2})

in v erse l a pl a ce \frac{3}{s ^{2} + 6 s + 10}