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Beliebt Rechnen >

integral of 1/(sqrt(x^2\pm a^2))

Lösung

\int \frac{1}{x ^{2} \pm a ^{2}} d x

Lösung

\frac{1}{\pm a ^{2}} ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} \pm a ^{2}} d x

\frac{1}{x ^{2} \pm a ^{2}} = \frac{1}{\pm a ^{2}} \frac{1}{x ^{2}}

= \int \frac{1}{\pm a ^{2}} \cdot \frac{1}{x ^{2}} d x

Entferne die Konstante:

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

= \frac{1}{\pm a ^{2}} \cdot \int \frac{1}{x ^{2}} d x

x^{2} = (x),

angenommen

x \geq 0

= \frac{1}{\pm a ^{2}} \cdot \int \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{\pm a ^{2}} ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{\pm a ^{2}} ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (0.3)/(rln(r))

\int \frac{0.3}{r ln ( r )} d r

integral of 1/(usqrt(u^2-1))

\int \frac{1}{u u ^{2} - 1} d u

integral of ((1-ln(x)))/x

\int \frac{( 1 - ln ( x ) )}{x} d x

integral of (3x^2+5)

\int (3 x^{2} + 5) d x

integral of 3ln(x)+3

\int 3 ln (x) + 3 d x