integral of ((x+5))/((x^2+16))

Lösung

\int \frac{( x + 5 )}{( x ^{2} + 16 )} d x

\frac{1}{2} ln x^{2} + 16 + \frac{5}{4} arctan (\frac{x}{4}) + C

Schritte zur Lösung

\int \frac{x + 5}{x ^{2} + 16} d x

Multipliziere aus

\frac{x + 5}{x ^{2} + 16} : \frac{x}{x ^{2} + 16} + \frac{5}{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{5}{x ^{2} + 16} d x

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

\int \frac{5}{x ^{2} + 16} d x = \frac{5}{4} arctan (\frac{x}{4})

= \frac{1}{2} ln x^{2} + 16 + \frac{5}{4} arctan (\frac{x}{4})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 16 + \frac{5}{4} arctan (\frac{x}{4}) + C

\int \frac{1}{x ^{3}} d x

x^{2} y^{^{''}} - 3 x y^{^{'}} + 3 y = 0

s l o p e x^{2} - 3 x - 4

d er i v a t i v e y = 7 x^{3}

\int \frac{x ^{2}}{1 - x ^{6}} d x