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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{x ^{7} e ^{x} - 8 x ^{6}}{x ^{7}} d x

\frac{d}{d x} (lo g_{18} (x^{2} - 5 x))

t a y l or \frac{x}{e ^{x} - 1}

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

n = 1 \sum \infty 1 0^{n} x^{n}