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Beliebt Rechnen >

integral of 1/(4-y^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende integrale Substitution an

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

Setze in

u = \frac{y}{2}

ein

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of sin^8(3x)cos^5(3x)

\int sin^{8} (3 x) cos^{5} (3 x) d x

derivative f(x)=ln(x^2-8x+16)

d er i v a t i v e f (x) = ln (x^{2} - 8 x + 16)

(\partial)/(\partial x)(cos^2(θ))

\frac{\partial}{\partial x} (cos^{2} (θ))

derivative of x^{(2/3})

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

(dy)/(dx)=6xe^y

\frac{d y}{d x} = 6 x e^{y}