integral of (x+8)/(x^2+16)

Lösung

\int \frac{x + 8}{x ^{2} + 16} d x

\frac{1}{2} ln x^{2} + 16 + 2 arctan (\frac{x}{4}) + C

Schritte zur Lösung

\int \frac{x + 8}{x ^{2} + 16} d x

Multipliziere aus

\frac{x + 8}{x ^{2} + 16} : \frac{x}{x ^{2} + 16} + \frac{8}{x ^{2} + 16}

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} + 16} d x + \int \frac{8}{x ^{2} + 16} d x

\int \frac{x}{x ^{2} + 16} d x = \frac{1}{2} ln x^{2} + 16

\int \frac{8}{x ^{2} + 16} d x = 2 arctan (\frac{x}{4})

= \frac{1}{2} ln x^{2} + 16 + 2 arctan (\frac{x}{4})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 16 + 2 arctan (\frac{x}{4}) + C

\frac{\partial}{\partial y} (3 x^{2} - 2 x y + 2)

\frac{\partial}{\partial x} (ln (\frac{3 x y}{5 z}))

\int (2 x + 1) x - 5 d x

a re a ∣ 4 x - 1 ∣, x^{2} - 5

\frac{d y}{d x} = - (\frac{y ^{2}}{1 + y ^{2}} e^{(- x)})