integral of ((x-1))/((x+4))

Lösung

\int \frac{( x - 1 )}{( x + 4 )} d x

- 5 ln ∣ x + 4 ∣ + x + C

Schritte zur Lösung

\int \frac{x - 1}{x + 4} d x

\frac{x - 1}{x + 4} = - \frac{5}{x + 4} + 1

= \int - \frac{5}{x + 4} + 1 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 + 4} d x + \int 1 d x

\int \frac{5}{x + 4} d x = 5 ln ∣ x + 4 ∣

\int 1 d x = x

= - 5 ln ∣ x + 4 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - 5 ln ∣ x + 4 ∣ + x + C

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

d er i v a t i v e f (x) = - \frac{x ^{3} + x - 1}{2}

\frac{d}{d x} (e^{2 x} + 2 + e^{- 2 x})

\frac{d}{d x} (\frac{1}{a} e^{a x})

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