integral of (3y^2-t^2)/(y^5)

Lösung

\int \frac{3 y ^{2} - t ^{2}}{y ^{5}} d y

\frac{t ^{2}}{4 y ^{4}} - \frac{3}{2 y ^{2}} + C

Schritte zur Lösung

\int \frac{3 y ^{2} - t ^{2}}{y ^{5}} d y

Multipliziere aus

\frac{- t ^{2} + 3 y ^{2}}{y ^{5}} : - \frac{t ^{2}}{y ^{5}} + \frac{3}{y ^{3}}

= \int - \frac{t ^{2}}{y ^{5}} + \frac{3}{y ^{3}} d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{t ^{2}}{y ^{5}} d y + \int \frac{3}{y ^{3}} d y

\int \frac{t ^{2}}{y ^{5}} d y = - \frac{t ^{2}}{4 y ^{4}}

\int \frac{3}{y ^{3}} d y = - \frac{3}{2 y ^{2}}

= - (- \frac{t ^{2}}{4 y ^{4}}) - \frac{3}{2 y ^{2}}

Vereinfache

= \frac{t ^{2}}{4 y ^{4}} - \frac{3}{2 y ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{t ^{2}}{4 y ^{4}} - \frac{3}{2 y ^{2}} + C

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