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)/(sqrt(x^2+2x+5))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

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

Vereinfache

2 (x^{2} + 2 x + 5 - ln (\frac{1}{2} x + 1 + x^{2} + 2 x + 5)) - 3 ln (\frac{1}{2} x + 1 + x^{2} + 2 x + 5) : 2 x^{2} + 2 x + 5 - 5 ln (\frac{1}{2} x + 1 + x^{2} + 2 x + 5)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (1-sec(x))/(cos(x)-1)

\int \frac{1 - sec ( x )}{cos ( x ) - 1} d x

integral of (24x)/(4x^2+1)

\int \frac{24 x}{4 x ^{2} + 1} d x

integral of (-1)/(4x)

\int \frac{- 1}{4 x} d x

integral of (-1)^{2x}

\int (- 1)^{2 x} d x

integral of ((sqrt(4-x^2))^3)/3

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