integral of (2x)/y-(3y^2)/(x^4)

Lösung

\int \frac{2 x}{y} - \frac{3 y ^{2}}{x ^{4}} d x

\frac{x ^{2}}{y} + \frac{y ^{2}}{x ^{3}} + C

Schritte zur Lösung

\int \frac{2 x}{y} - \frac{3 y ^{2}}{x ^{4}} d x

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{2 x}{y} d x - \int \frac{3 y ^{2}}{x ^{4}} d x

\int \frac{2 x}{y} d x = \frac{x ^{2}}{y}

\int \frac{3 y ^{2}}{x ^{4}} d x = - \frac{y ^{2}}{x ^{3}}

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

Vereinfache

= \frac{x ^{2}}{y} + \frac{y ^{2}}{x ^{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{y} + \frac{y ^{2}}{x ^{3}} + C

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