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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4} (ln ∣ 2 x + 1 ∣ - ln ∣ 2 x - 1 ∣) + C

Schritte zur Lösung

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

Wende integrale Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Setze in

u = 2 x

ein

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

Vereinfache

\frac{1}{2} (\frac{ln ∣ 2 x + 1 ∣}{2} - \frac{ln ∣ 2 x - 1 ∣}{2}) : \frac{1}{4} (ln ∣ 2 x + 1 ∣ - ln ∣ 2 x - 1 ∣)

= \frac{1}{4} (ln ∣ 2 x + 1 ∣ - ln ∣ 2 x - 1 ∣)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} (ln ∣ 2 x + 1 ∣ - ln ∣ 2 x - 1 ∣) + C

Graph

Beliebte Beispiele

tangent f(x)=-5-3x^2,-53,\at x=4

t an g e n t f (x) = - 5 - 3 x^{2}, - 53, at x = 4

steigung (-3.2)(7.6)

s l o p e (- 3.2) (7.6)

integral of x^2(x^3-1)^{10}

\int x^{2} (x^{3} - 1)^{10} d x

limit as x approaches-3 of 7/(x^7)

x \to - 3 lim (\frac{7}{x ^{7}})

integral of xsqrt(2)

\int x 2 d x