de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((2x+3))/(4x^2+4x+5)

Lösung

\int \frac{( 2 x + 3 )}{4 x ^{2} + 4 x + 5} d x

Lösung

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

Schritte zur Lösung

\int \frac{2 x + 3}{4 x ^{2} + 4 x + 5} d x

Multipliziere aus

\frac{2 x + 3}{4 x ^{2} + 4 x + 5} : \frac{2 x}{4 x ^{2} + 4 x + 5} + \frac{3}{4 x ^{2} + 4 x + 5}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2 x}{4 x ^{2} + 4 x + 5} d x + \int \frac{3}{4 x ^{2} + 4 x + 5} d x

\int \frac{2 x}{4 x ^{2} + 4 x + 5} d x = \frac{1}{4} ln 4 x^{2} + 4 x + 5 - \frac{1}{4} arctan (x + \frac{1}{2})

\int \frac{3}{4 x ^{2} + 4 x + 5} d x = \frac{3}{4} arctan (x + \frac{1}{2})

= \frac{1}{4} ln 4 x^{2} + 4 x + 5 - \frac{1}{4} arctan (x + \frac{1}{2}) + \frac{3}{4} arctan (x + \frac{1}{2})

Addiere gleiche Elemente:

- \frac{1}{4} arctan (x + \frac{1}{2}) + \frac{3}{4} arctan (x + \frac{1}{2}) = \frac{1}{2} arctan (x + \frac{1}{2})

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (18s+18)/((s^2+1)(s-1)^3)

\int \frac{18 s + 18}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

integral of 2/(sqrt(9-4x))

\int \frac{2}{9 - 4 x} d x

integral of-4x^7sin(x^8)

\int - 4 x^{7} sin (x^{8}) d x

integral of 9tan(x)sec^7(x)

\int 9 tan (x) sec^{7} (x) d x

integral of ((x^4-5x^3+7x)/x)

\int (\frac{x ^{4} - 5 x ^{3} + 7 x}{x}) d x