de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

\int (1 + (4 x + 2)^{2}) d x

Lösung

\frac{1}{8} (2 (2 x + 1) 16 x^{2} + 16 x + 5 + ln 4 x + 2 + 16 x^{2} + 16 x + 5) + C

Schritte zur Lösung

\int 1 + (4 x + 2)^{2} d x

Wende U-Substitution an

= \int \frac{1 + u ^{2}}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int 1 + u^{2} d u

Trigonometrische Substitution anwenden

= \frac{1}{4} \cdot \int sec^{3} (v) d v

Wende integrale Reduktion an

= \frac{1}{4} (\frac{sec ^{2} ( v ) sin ( v )}{2} + \frac{1}{2} \cdot \int sec (v) d v)

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

= \frac{1}{4} (\frac{sec ^{2} ( v ) sin ( v )}{2} + \frac{1}{2} ln ∣ tan (v) + sec (v) ∣)

Ersetze zurück

= \frac{1}{4} (\frac{sec ^{2} ( arctan ( 4 x + 2 ) ) sin ( arctan ( 4 x + 2 ) )}{2} + \frac{1}{2} ln ∣ tan (arctan (4 x + 2)) + sec (arctan (4 x + 2)) ∣)

Vereinfache

\frac{1}{4} (\frac{sec ^{2} ( arctan ( 4 x + 2 ) ) sin ( arctan ( 4 x + 2 ) )}{2} + \frac{1}{2} ln ∣ tan (arctan (4 x + 2)) + sec (arctan (4 x + 2)) ∣) : \frac{1}{8} (2 (2 x + 1) 16 x^{2} + 16 x + 5 + ln 4 x + 2 + 16 x^{2} + 16 x + 5)

= \frac{1}{8} (2 (2 x + 1) 16 x^{2} + 16 x + 5 + ln 4 x + 2 + 16 x^{2} + 16 x + 5)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{8} (2 (2 x + 1) 16 x^{2} + 16 x + 5 + ln 4 x + 2 + 16 x^{2} + 16 x + 5) + C

Graph

Beliebte Beispiele

integral of (5x^2+2xe^x-1)/x

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

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

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

integral of tan^4(x)*sec^4(x)

\int tan^{4} (x) \cdot sec^{4} (x) d x

integral of 18θsin(18θ^2)

\int 18 θ sin (18 θ^{2}) d θ

integral of (sin(x))^2*(cos(x))^2

\int (sin (x))^{2} \cdot (cos (x))^{2} d x