integral from 1 to 5 of (e^{x/2})/(x^3)

Lösung

\int_{1}^{5} \frac{e ^{\frac{x}{2}}}{x ^{3}} d x

\frac{- 14 e ^{\frac{5}{2}} + 25 Ei ( \frac{5}{2} )}{200} - \frac{- 6 e ^{\frac{1}{2}} + Ei ( \frac{1}{2} )}{8}

Schritte zur Lösung

\int_{1}^{5} \frac{e ^{\frac{x}{2}}}{x ^{3}} d x

Wende die partielle Integration an

= [- \frac{e ^{\frac{x}{2}}}{2 x ^{2}} - \int - \frac{e ^{\frac{x}{2}}}{4 x ^{2}} d x]_{1}^{5}

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

= [- \frac{e ^{\frac{x}{2}}}{2 x ^{2}} - (- \frac{1}{4} (- \frac{e ^{\frac{x}{2}}}{x} + \frac{1}{2} Ei (\frac{x}{2})))]_{1}^{5}

Vereinfache

= [- \frac{e ^{\frac{x}{2}}}{2 x ^{2}} + \frac{1}{4} (- \frac{e ^{\frac{x}{2}}}{x} + \frac{1}{2} Ei (\frac{x}{2}))]_{1}^{5}

Berechne die Grenzen:

\frac{- 14 e ^{\frac{5}{2}} + 25 Ei ( \frac{5}{2} )}{200} - \frac{- 6 e ^{\frac{1}{2}} + Ei ( \frac{1}{2} )}{8}

= \frac{- 14 e ^{\frac{5}{2}} + 25 Ei ( \frac{5}{2} )}{200} - \frac{- 6 e ^{\frac{1}{2}} + Ei ( \frac{1}{2} )}{8}

a re a 3 e^{x}, 3 x e^{x^{2}}, [0, 1]

x \to 6 lim (2 x - 7)

\int \frac{( x + 6 )}{( x + 1 )} d x

\int_{2}^{3} \frac{ln ( 2 x ^{5} )}{x ^{2}} d x

\frac{\partial}{\partial x} (x^{a} y^{1 - a})