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Beliebt Rechnen >

integral of 1/(sqrt(4^2-x^2))

Lösung

\int \frac{1}{4 ^{2} - x ^{2}} d x

Lösung

arcsin (\frac{1}{4} x) + C

Schritte zur Lösung

\int \frac{1}{4 ^{2} - x ^{2}} d x

4^{2} - x^{2} = 4^{2} (1 - \frac{x ^{2}}{4 ^{2}})

= \int \frac{1}{4 ^{2} ( 1 - \frac{x ^{2}}{4 ^{2}} )} d x

Vereinfache

\frac{1}{4 ^{2} ( 1 - \frac{x ^{2}}{4 ^{2}} )} : \frac{1}{16 - x ^{2}}

= \int \frac{1}{16 - x ^{2}} d x

Trigonometrische Substitution anwenden

= \int 1 d u

Integral einer Konstanten :

\int a d x = a x

= 1 \cdot u

Setze in

u = arcsin (\frac{1}{4} x)

ein

= 1 \cdot arcsin (\frac{1}{4} x)

Vereinfache

= arcsin (\frac{1}{4} x)

Füge eine Konstante zur Lösung hinzu

= arcsin (\frac{1}{4} x) + C

Graph

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