integral of (3x^2+9x^4-x)/(x^2)

Lösung

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

3 x + 3 x^{3} - ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{3 x ^{2} + 9 x ^{4} - x}{x ^{2}} : 3 + 9 x^{2} - \frac{1}{x}

= \int 3 + 9 x^{2} - \frac{1}{x} 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 3 d x + \int 9 x^{2} d x - \int \frac{1}{x} d x

\int 3 d x = 3 x

\int 9 x^{2} d x = 3 x^{3}

\int \frac{1}{x} d x = ln ∣ x ∣

= 3 x + 3 x^{3} - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 3 x + 3 x^{3} - ln ∣ x ∣ + C

\int tanh (\frac{x}{7}) d x

\int x arctanh (x) d x

\int tan^{6} (5 x) d x

\int y^{4} e^{- y} d y

\int \frac{5}{3 a d} d y