de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (3+7x)/(1+x^2)

Lösung

\int \frac{3 + 7 x}{1 + x ^{2}} d x

Lösung

3 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{3 + 7 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{3 + 7 x}{1 + x ^{2}} : \frac{3}{1 + x ^{2}} + \frac{7 x}{1 + x ^{2}}

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{3}{1 + x ^{2}} d x + \int \frac{7 x}{1 + x ^{2}} d x

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

\int \frac{7 x}{1 + x ^{2}} d x = \frac{7}{2} ln 1 + x^{2}

= 3 arctan (x) + \frac{7}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 3 arctan (x) + \frac{7}{2} ln 1 + x^{2} + C

Graph

Beliebte Beispiele

integral of-(x^2-2x^5)(x^3-x^6)^{-10}

\int - (x^{2} - 2 x^{5}) (x^{3} - x^{6})^{- 10} d x

integral of 3x^2ln(x^2+3)

\int 3 x^{2} ln (x^{2} + 3) d x

integral of x(2x-1)^2

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

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

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

integral of x/(x^2-x)

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