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

Lösung

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

- ln ∣ x ∣ - ln (2) x - \frac{1}{x} + C

Schritte zur Lösung

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

\int \frac{- 1}{x} d x = - ln ∣ x ∣

\int ln (2) d x = ln (2) x

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

= - ln ∣ x ∣ - ln (2) x - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x ∣ - ln (2) x - \frac{1}{x} + C

\int \frac{3}{x ^{2} + 14 x + 97} d x

\int cos (\frac{1}{5} t) d t

\int 4 x^{2} + 8 x + 5 d x

\int (\frac{5}{x})^{2} d x

\int \frac{3 x - 2}{x - 1} d x