integral of (5/(x+2)-3/((x+2)^2))

Lösung

\int (\frac{5}{x + 2} - \frac{3}{( x + 2 ) ^{2}}) d x

5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + C

Schritte zur Lösung

\int \frac{5}{x + 2} - \frac{3}{( x + 2 ) ^{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{5}{x + 2} d x - \int \frac{3}{( x + 2 ) ^{2}} d x

\int \frac{5}{x + 2} d x = 5 ln ∣ x + 2 ∣

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

= 5 ln ∣ x + 2 ∣ - (- \frac{3}{x + 2})

Vereinfache

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2}

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + C

\int \frac{- e ^{2 x}}{e ^{x} + 1} d x

\int x^{3} (e^{3 x^{2}}) d x

\int \frac{5}{2 x - 4} d x

\int \frac{1}{28 - x ^{2}} d x

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