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

Lösung

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

x + 2 ln ∣ x ∣ - \frac{1}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= x + 2 ln ∣ x ∣ - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= x + 2 ln ∣ x ∣ - \frac{1}{x} + C

\int 3 sin^{2} (t) d t

y^{^{'''}} + 6 y^{^{''}} + 11 y^{^{'}} + 6 y = 0

(9 y^{2} - x y) d x + (x^{2}) d y = 0

\int \frac{x ^{3}}{x ^{2} + 9} d x

d er i v a t i v e 4^{- 3} (\frac{2}{s ^{7}} + 3 s)^{4}