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Beliebt Rechnen >

integral of 6arctan(8/x)

Lösung

\int 6 arctan (\frac{8}{x}) d x

Lösung

6 (x arctan (\frac{8}{x}) + 4 ln 64 + x^{2}) + C

Schritte zur Lösung

\int 6 arctan (\frac{8}{x}) d x

Entferne die Konstante:

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

= 6 \cdot \int arctan (\frac{8}{x}) d x

Wende die partielle Integration an

= 6 (x arctan (\frac{8}{x}) - \int - \frac{8 x}{64 + x ^{2}} d x)

\int - \frac{8 x}{64 + x ^{2}} d x = - 4 ln 64 + x^{2}

= 6 (x arctan (\frac{8}{x}) - (- 4 ln 64 + x^{2}))

Vereinfache

= 6 (x arctan (\frac{8}{x}) + 4 ln 64 + x^{2})

Füge eine Konstante zur Lösung hinzu

= 6 (x arctan (\frac{8}{x}) + 4 ln 64 + x^{2}) + C

Graph

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