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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int x 8 - 2 x^{2} d x

\int \frac{- 2 x + 11}{x ^{2} - 8 x + 25} d x

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

\int (\frac{1}{x + 2}) d x

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