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)/(x^2+2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende integrale Substitution an

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

Multipliziere aus

\frac{u + 2}{u ^{2} + 1} : \frac{u}{u ^{2} + 1} + \frac{2}{u ^{2} + 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{u}{u ^{2} + 1} d u + \int \frac{2}{u ^{2} + 1} d u

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

\int \frac{2}{u ^{2} + 1} d u = 2 arctan (u)

= \frac{1}{2} ln u^{2} + 1 + 2 arctan (u)

Setze in

u = \frac{x}{2}

ein

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

(\frac{x}{2})^{2} = \frac{x ^{2}}{2}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 1/((60-x)(150-x))

\int \frac{1}{( 60 - x ) ( 150 - x )} d x

integral of ((cos(x)))/((4-sin^2(x)))

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

integral of y^{-1}+3/x

\int y^{- 1} + \frac{3}{x} d x

integral of (6x^2)(x^{1/4})

\int (6 x^{2}) (x^{\frac{1}{4}}) d x

integral of 1/(6x+2)

\int \frac{1}{6 x + 2} d x