integral of (x+3)/(x^2+25)

Lösung

\int \frac{x + 3}{x ^{2} + 25} d x

\frac{1}{2} ln x^{2} + 25 + \frac{3}{5} arctan (\frac{x}{5}) + C

Schritte zur Lösung

\int \frac{x + 3}{x ^{2} + 25} d x

Multipliziere aus

\frac{x + 3}{x ^{2} + 25} : \frac{x}{x ^{2} + 25} + \frac{3}{x ^{2} + 25}

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} + 25} d x + \int \frac{3}{x ^{2} + 25} d x

\int \frac{x}{x ^{2} + 25} d x = \frac{1}{2} ln x^{2} + 25

\int \frac{3}{x ^{2} + 25} d x = \frac{3}{5} arctan (\frac{x}{5})

= \frac{1}{2} ln x^{2} + 25 + \frac{3}{5} arctan (\frac{x}{5})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 25 + \frac{3}{5} arctan (\frac{x}{5}) + C

x \to 6 lim (\frac{1 - x}{6 - x})

\int_{3}^{5} 3 x d x

t a y l or x^{2}

y^{^{'}} - \frac{9}{x} y = \frac{( y ^{4} )}{x ^{16}}, y (1) = 1

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