integral of ((x-1))/x

Lösung

\int \frac{( x - 1 )}{x} d x

x - ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x - 1}{x} d x

Multipliziere aus

\frac{x - 1}{x} : 1 - \frac{1}{x}

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= x - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= x - ln ∣ x ∣ + C

d o main f (x) = (3 x^{2})^{2 x} (x^{2} + 2 x)^{2}

y^{^{''}} - 6 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 9

\frac{d y}{d t} = \frac{1}{5} t

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 12, y^{^{'}} (0) = b

\frac{d}{d x} ((\frac{x ^{2}}{8} + x - \frac{1}{x})^{4})