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Beliebt Rechnen >

integral of 1/(x(64x^2-1)^{1/2)}

Lösung

\int \frac{1}{x ( 64 x ^{2} - 1 ) ^{\frac{1}{2}}} d x

Lösung

arctan ((64 x^{2} - 1)^{\frac{1}{2}}) + C

Schritte zur Lösung

\int \frac{1}{x ( 64 x ^{2} - 1 ) ^{\frac{1}{2}}} d x

Wende U-Substitution an

= \int \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= arctan (u)

Setze in

u = (64 x^{2} - 1)^{\frac{1}{2}}

ein

= arctan ((64 x^{2} - 1)^{\frac{1}{2}})

Füge eine Konstante zur Lösung hinzu

= arctan ((64 x^{2} - 1)^{\frac{1}{2}}) + C

Graph

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