integral of x/((x+1)^{5/2)}

Lösung

\int \frac{x}{( x + 1 ) ^{\frac{5}{2}}} d x

- \frac{2 x}{3 ( x + 1 ) ^{\frac{3}{2}}} - \frac{4}{3 ( x + 1 ) ^{\frac{1}{2}}} + C

Schritte zur Lösung

\int \frac{x}{( x + 1 ) ^{\frac{5}{2}}} d x

Wende die partielle Integration an

= - \frac{2 x}{3 ( x + 1 ) ^{\frac{3}{2}}} - \int - \frac{2}{3 ( x + 1 ) ^{\frac{3}{2}}} d x

\int - \frac{2}{3 ( x + 1 ) ^{\frac{3}{2}}} d x = \frac{4}{3 ( x + 1 ) ^{\frac{1}{2}}}

= - \frac{2 x}{3 ( x + 1 ) ^{\frac{3}{2}}} - \frac{4}{3 ( x + 1 ) ^{\frac{1}{2}}}

Füge eine Konstante zur Lösung hinzu

= - \frac{2 x}{3 ( x + 1 ) ^{\frac{3}{2}}} - \frac{4}{3 ( x + 1 ) ^{\frac{1}{2}}} + C

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