integral of (8x+1)/(x^2+1)

Lösung

\int \frac{8 x + 1}{x ^{2} + 1} d x

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

Schritte zur Lösung

\int \frac{8 x + 1}{x ^{2} + 1} d x

Multipliziere aus

\frac{8 x + 1}{x ^{2} + 1} : \frac{8 x}{x ^{2} + 1} + \frac{1}{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{8 x}{x ^{2} + 1} d x + \int \frac{1}{x ^{2} + 1} d x

\int \frac{8 x}{x ^{2} + 1} d x = 4 ln x^{2} + 1

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

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

Füge eine Konstante zur Lösung hinzu

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

t an g e n t f (x) = \frac{8}{x}, at x = 5

y^{^{''}} + y = 9 sin (x)

d er i v a t i v e 40 ln (3 x + 1) - \frac{x}{3}

\int 3 x - 5 d x

\int \frac{1}{13 - 5 cos ( x )} d x