integral of ((6+6x))/(1+x^2)

Lösung

\int \frac{( 6 + 6 x )}{1 + x ^{2}} d x

6 arctan (x) + 3 ln 1 + x^{2} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{6 + 6 x}{1 + x ^{2}} : \frac{6}{1 + x ^{2}} + \frac{6 x}{1 + x ^{2}}

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

\int \frac{6}{1 + x ^{2}} d x = 6 arctan (x)

\int \frac{6 x}{1 + x ^{2}} d x = 3 ln 1 + x^{2}

= 6 arctan (x) + 3 ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 6 arctan (x) + 3 ln 1 + x^{2} + C

\int x^{2} cos (x) + 2 sin (x) d x

\int 21 e^{42 x} arctan (e^{21 x}) d x

\int 7 (t^{5} - t^{3} + 1) d t

s l o p e (- 3.3) (- 3.13)

d er i v a t i v e \frac{x}{x ^{3}}