integral of (z^4+10z^2+25)/(z^3+5z)

Lösung

\int \frac{z ^{4} + 10 z ^{2} + 25}{z ^{3} + 5 z} d z

\frac{z ^{2}}{2} + 5 ln ∣ z ∣ + C

Schritte zur Lösung

\int \frac{z ^{4} + 10 z ^{2} + 25}{z ^{3} + 5 z} d z

Vereinfache

\frac{z ^{4} + 10 z ^{2} + 25}{z ^{3} + 5 z} : \frac{z ^{2} + 5}{z}

= \int \frac{z ^{2} + 5}{z} d z

Multipliziere aus

\frac{z ^{2} + 5}{z} : z + \frac{5}{z}

= \int z + \frac{5}{z} d z

Wende die Summenregel an:

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

= \int z d z + \int \frac{5}{z} d z

\int z d z = \frac{z ^{2}}{2}

\int \frac{5}{z} d z = 5 ln ∣ z ∣

= \frac{z ^{2}}{2} + 5 ln ∣ z ∣

Füge eine Konstante zur Lösung hinzu

= \frac{z ^{2}}{2} + 5 ln ∣ z ∣ + C

\int_{0}^{\frac{π}{4}} (tan^{2} (x)) d x

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

2 y^{^{''}} + 20 y^{^{'}} + 50 y = 0

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