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Beliebt Rechnen >

integral of ((16-t^2)^{3/2})/(t^6)

Lösung

\int \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{t ^{6}} d t

Lösung

- \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} + \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}} + C

Schritte zur Lösung

\int \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{t ^{6}} d t

Wende die partielle Integration an

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} - \int \frac{3 ( - t ^{2} + 16 ) ^{\frac{1}{2}}}{5 t ^{4}} d t

\int \frac{3 ( - t ^{2} + 16 ) ^{\frac{1}{2}}}{5 t ^{4}} d t = - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}}

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} - - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}}

Vereinfache

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} + \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{5 t ^{5}} + \frac{( 16 - t ^{2} ) ^{\frac{3}{2}}}{80 t ^{3}} + C

Graph

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