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}

Füge eine Konstante zur Lösung hinzu

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

\int \frac{( 2 x + 1 )}{( x ^{2} + 9 )} d x

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

\int \frac{1}{5 - 2 x ^{2}} d x

\int \frac{2 x + 5}{- x ^{2} - 6 x + 16} d x

\int e^{\frac{1}{50} t} d t