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Beliebt Rechnen >

integral of 1/(sqrt((x+1)^2+25))

Lösung

\int \frac{1}{( x + 1 ) ^{2} + 25} d x

Lösung

ln (\frac{1}{5} x + 1 + x^{2} + 2 x + 26) + C

Schritte zur Lösung

\int \frac{1}{( x + 1 ) ^{2} + 25} d x

Wende U-Substitution an

= \int \frac{1}{u ^{2} + 25} d u

Trigonometrische Substitution anwenden

= \int sec (v) d v

Nutze das gemeinsame Integral :

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

= ln ∣ tan (v) + sec (v) ∣

Ersetze zurück

= ln tan (arctan (\frac{1}{5} (x + 1))) + sec (arctan (\frac{1}{5} (x + 1)))

Vereinfache

ln tan (arctan (\frac{1}{5} (x + 1))) + sec (arctan (\frac{1}{5} (x + 1))) : ln (\frac{1}{5} x + 1 + x^{2} + 2 x + 26)

= ln (\frac{1}{5} x + 1 + x^{2} + 2 x + 26)

Füge eine Konstante zur Lösung hinzu

= ln (\frac{1}{5} x + 1 + x^{2} + 2 x + 26) + C

Graph

Beliebte Beispiele

integral from 1 to 3 of xe^{x^2}

\int_{1}^{3} x e^{x^{2}} d x

derivative of arccos(1-2x^2)

\frac{d}{d x} (arccos (1 - 2 x^{2}))

fläche y=6-6x,y=0,x=0

a re a y = 6 - 6 x, y = 0, x = 0

(\partial)/(\partial x)(-x^2+2xy-y^2)

\frac{\partial}{\partial x} (- x^{2} + 2 x y - y^{2})

integral of csc^4(3x)

\int csc^{4} (3 x) d x