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Beliebt Rechnen >

integral of 1/(sqrt((a^2+v^2)))

Lösung

\int \frac{1}{( a ^{2} + v ^{2} )} d v

Lösung

ln (\frac{v + a ^{2} + v ^{2}}{∣ a ∣}) + C

Schritte zur Lösung

\int \frac{1}{a ^{2} + v ^{2}} d v

Trigonometrische Substitution anwenden

= \int sec (u) d u

Nutze das gemeinsame Integral :

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= ln ∣ tan (u) + sec (u) ∣

Setze in

u = arctan (\frac{1}{a} v)

ein

= ln tan (arctan (\frac{1}{a} v)) + sec (arctan (\frac{1}{a} v))

Vereinfache

ln tan (arctan (\frac{1}{a} v)) + sec (arctan (\frac{1}{a} v)) : ln (\frac{v + a ^{2} + v ^{2}}{∣ a ∣})

= ln (\frac{v + a ^{2} + v ^{2}}{∣ a ∣})

Füge eine Konstante zur Lösung hinzu

= ln (\frac{v + a ^{2} + v ^{2}}{∣ a ∣}) + C

Graph

Beliebte Beispiele

y^'+tan(x)y-sin(x)=0

y^{^{'}} + tan (x) y - sin (x) = 0

integral of 1/x+2x

\int \frac{1}{x} + 2 x d x

(\partial)/(\partial x)(4sin(4x))

\frac{\partial}{\partial x} (4 sin (4 x))

derivative of arccos(x+y)

\frac{d}{d x} (arccos (x + y))

tangent f(x)=3x^2,\at x=(6)

t an g e n t f (x) = 3 x^{2}, at x = (6)