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Beliebt Rechnen >

integral of 1/(9-4x^2)

Lösung

\int \frac{1}{9 - 4 x ^{2}} d x

Lösung

\frac{1}{12} (ln \frac{2}{3} x + 1 - ln \frac{2}{3} x - 1) + C

Schritte zur Lösung

\int \frac{1}{9 - 4 x ^{2}} d x

Wende integrale Substitution an

= \int \frac{1}{6 ( - u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int \frac{1}{- u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{6} (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2})

Setze in

u = \frac{2}{3} x

ein

= \frac{1}{6} (\frac{ln \frac{2}{3} x + 1}{2} - \frac{ln \frac{2}{3} x - 1}{2})

Vereinfache

\frac{1}{6} (\frac{ln \frac{2}{3} x + 1}{2} - \frac{ln \frac{2}{3} x - 1}{2}) : \frac{1}{12} (ln \frac{2}{3} x + 1 - ln \frac{2}{3} x - 1)

= \frac{1}{12} (ln \frac{2}{3} x + 1 - ln \frac{2}{3} x - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} (ln \frac{2}{3} x + 1 - ln \frac{2}{3} x - 1) + C

Graph

Beliebte Beispiele

integral from 0 to infinity of f(a+x)

\int_{0}^{\infty} f (a + x) d x

sum from n=0 to infinity of 3/((1+i)^n)

n = 0 \sum \infty \frac{3}{( 1 + i ) ^{n}}

implicit (dy)/(dx),e^y=x

im pl i c i t \frac{d y}{d x}, e^{y} = x

d/(du)(usin(v))

\frac{d}{d u} (u sin (v))

derivative of 3+x^2

\frac{d}{d x} (3 + x^{2})