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

Lösung

\int (\frac{9}{x} - \frac{4}{x ^{3}}) d x

9 ln ∣ x ∣ + \frac{2}{x ^{2}} + C

Schritte zur Lösung

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

\int \frac{9}{x} d x = 9 ln ∣ x ∣

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

= 9 ln ∣ x ∣ - (- \frac{2}{x ^{2}})

Vereinfache

= 9 ln ∣ x ∣ + \frac{2}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= 9 ln ∣ x ∣ + \frac{2}{x ^{2}} + C

\frac{d}{d θ} (cos (θ) - sin (θ))

im pl i c i t \frac{d y}{d x}, y^{3} = x^{4}

\frac{\partial}{\partial x} (\frac{x}{y} + e^{y})

\int sin (3 x) cos (x) d x

\int \frac{π}{4} x - x arctan (x) d x