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Beliebt Rechnen >

integral of x/((x^2+1)^{7/2)}

Lösung

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{7}{2}}} d x

Lösung

- \frac{1}{5 ( x ^{2} + 1 ) ^{\frac{5}{2}}} + C

Schritte zur Lösung

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{7}{2}}} d x

Wende U-Substitution an

= \int \frac{1}{2 ( u + 1 ) ^{\frac{7}{2}}} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{1}{( u + 1 ) ^{\frac{7}{2}}} d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int \frac{1}{v ^{\frac{7}{2}}} d v

Wende die Potenzregel an

= \frac{1}{2} (- \frac{2}{5 v ^{\frac{5}{2}}})

Ersetze zurück

= \frac{1}{2} (- \frac{2}{5 ( x ^{2} + 1 ) ^{\frac{5}{2}}})

Vereinfache

\frac{1}{2} (- \frac{2}{5 ( x ^{2} + 1 ) ^{\frac{5}{2}}}) : - \frac{1}{5 ( x ^{2} + 1 ) ^{\frac{5}{2}}}

= - \frac{1}{5 ( x ^{2} + 1 ) ^{\frac{5}{2}}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5 ( x ^{2} + 1 ) ^{\frac{5}{2}}} + C

Graph

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