integral of (y+1)/(y^3)

Lösung

\int \frac{y + 1}{y ^{3}} d y

- \frac{1}{y} - \frac{1}{2 y ^{2}} + C

Schritte zur Lösung

\int \frac{y + 1}{y ^{3}} d y

Multipliziere aus

\frac{y + 1}{y ^{3}} : \frac{1}{y ^{2}} + \frac{1}{y ^{3}}

= \int \frac{1}{y ^{2}} + \frac{1}{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{1}{y ^{2}} d y + \int \frac{1}{y ^{3}} d y

\int \frac{1}{y ^{2}} d y = - \frac{1}{y}

\int \frac{1}{y ^{3}} d y = - \frac{1}{2 y ^{2}}

= - \frac{1}{y} - \frac{1}{2 y ^{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{y} - \frac{1}{2 y ^{2}} + C

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