integral of (x+5)/(x^2+25)

Lösung

\int \frac{x + 5}{x ^{2} + 25} d x

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

Schritte zur Lösung

\int \frac{x + 5}{x ^{2} + 25} d x

Multipliziere aus

\frac{x + 5}{x ^{2} + 25} : \frac{x}{x ^{2} + 25} + \frac{5}{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{5}{x ^{2} + 25} d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{9 x ^{2} - 8 x + 24}{x ^{3} + 4 x} d x

x y^{^{'}} - y = x^{2} + 2 x + 1

\int x^{3} (4 x^{2} + 5) d x

in v erse l a pl a ce \frac{6 ( s + 34 )}{s ( s ^{2} + 10 s + 34 )}

n or ma l f (x) = x^{4} + 5 e^{x}, (0, 5)