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Beliebt Rechnen >

integral of sec(1/2)ztan(1/2)z

Lösung

\int sec (\frac{1}{2}) z tan (\frac{1}{2}) z d z

Lösung

\frac{1}{3} sec (\frac{1}{2}) tan (\frac{1}{2}) z^{3} + C

Schritte zur Lösung

\int sec (\frac{1}{2}) z tan (\frac{1}{2}) z d z

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sec (\frac{1}{2}) tan (\frac{1}{2}) \cdot \int zz d z

Vereinfache

zz : z^{2}

= sec (\frac{1}{2}) tan (\frac{1}{2}) \cdot \int z^{2} d z

Wende die Potenzregel an

= sec (\frac{1}{2}) tan (\frac{1}{2}) \frac{z ^{3}}{3}

Vereinfache

sec (\frac{1}{2}) tan (\frac{1}{2}) \frac{z ^{3}}{3} : \frac{1}{3} sec (\frac{1}{2}) tan (\frac{1}{2}) z^{3}

= \frac{1}{3} sec (\frac{1}{2}) tan (\frac{1}{2}) z^{3}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} sec (\frac{1}{2}) tan (\frac{1}{2}) z^{3} + C

Graph

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