de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4} ln 16 x^{2} + 8 x + 8 + \frac{7}{2} arctan (\frac{1}{7} (4 x + 1)) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 2}{2 x ^{2} + x + 1} : \frac{x}{2 x ^{2} + x + 1} + \frac{2}{2 x ^{2} + x + 1}

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

\int \frac{x}{2 x ^{2} + x + 1} d x = 2 (\frac{1}{8} ln 16 x^{2} + 8 x + 8 - \frac{1}{4 7} arctan (\frac{4 x + 1}{7}))

\int \frac{2}{2 x ^{2} + x + 1} d x = \frac{4}{7} arctan (\frac{4 x + 1}{7})

= 2 (\frac{1}{8} ln 16 x^{2} + 8 x + 8 - \frac{1}{4 7} arctan (\frac{4 x + 1}{7})) + \frac{4}{7} arctan (\frac{4 x + 1}{7})

Vereinfache

2 (\frac{1}{8} ln 16 x^{2} + 8 x + 8 - \frac{1}{4 7} arctan (\frac{4 x + 1}{7})) + \frac{4}{7} arctan (\frac{4 x + 1}{7}) : \frac{1}{4} ln 16 x^{2} + 8 x + 8 + \frac{7}{2} arctan (\frac{1}{7} (4 x + 1))

= \frac{1}{4} ln 16 x^{2} + 8 x + 8 + \frac{7}{2} arctan (\frac{1}{7} (4 x + 1))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} ln 16 x^{2} + 8 x + 8 + \frac{7}{2} arctan (\frac{1}{7} (4 x + 1)) + C

Graph

Beliebte Beispiele

integral of csc(x)csc^2(x)

\int csc (x) csc^{2} (x) d x

integral of (ln(x))/(5x^2)

\int \frac{ln ( x )}{5 x ^{2}} d x

integral of (2x^5+3x^4+6x^3-7x^2)/(x^2)

\int \frac{2 x ^{5} + 3 x ^{4} + 6 x ^{3} - 7 x ^{2}}{x ^{2}} d x

integral of xsqrt(196-49x^2)

\int x 196 - 49 x^{2} d x

integral of ((2x+8))/((x^2+2x+5)^2)

\int \frac{( 2 x + 8 )}{( x ^{2} + 2 x + 5 ) ^{2}} d x