integral of (x+2+3/x)

Lösung

\int (x + 2 + \frac{3}{x}) d x

\frac{x ^{2}}{2} + 2 x + 3 ln ∣ x ∣ + C

Schritte zur Lösung

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

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

\int 2 d x = 2 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{x ^{2}}{2} + 2 x + 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + 2 x + 3 ln ∣ x ∣ + C

\int_{0}^{π} sec^{2} (\frac{x}{3}) d x

e^{- x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

\int \frac{4 e ^{3 x}}{1 + e ^{3 x}} d x

im pl i c i t \frac{d y}{d x}, 2 x^{2} + 2 x + x y = 1

\frac{\partial}{\partial x} (A^{2} x^{2} + B^{2} y^{2})