de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/(sqrt(4x^2+5))

Lösung

\int \frac{1}{4 x ^{2} + 5} d x

Lösung

\frac{1}{2} ln \frac{2}{5} x + \frac{1}{5} (5 + 4 x^{2}) + C

Schritte zur Lösung

\int \frac{1}{4 x ^{2} + 5} d x

Trigonometrische Substitution anwenden

= \int \frac{sec ( 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 sec (u) d u

Nutze das gemeinsame Integral :

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

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

Setze in

u = arctan (\frac{2}{5} x)

ein

= \frac{1}{2} ln tan (arctan (\frac{2}{5} x)) + sec (arctan (\frac{2}{5} x))

Vereinfache

\frac{1}{2} ln tan (arctan (\frac{2}{5} x)) + sec (arctan (\frac{2}{5} x)) : \frac{1}{2} ln \frac{2}{5} x + \frac{1}{5} (5 + 4 x^{2})

= \frac{1}{2} ln \frac{2}{5} x + \frac{1}{5} (5 + 4 x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln \frac{2}{5} x + \frac{1}{5} (5 + 4 x^{2}) + C

Graph

Beliebte Beispiele

limit as x approaches 0 of cos(pi)x

x \to 0 lim (cos (π) x)

integral of 3x^{-2/3}

\int 3 x^{- \frac{2}{3}} d x

integral of e^{2x}(sin(3x))

\int e^{2 x} (sin (3 x)) d x

derivative f(x)=e^x-x^8

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

tangent f(x)=4x+x^2,\at x=0

t an g e n t f (x) = 4 x + x^{2}, at x = 0