integral of x/((x+3))

Lösung

\int \frac{x}{( x + 3 )} d x

x + 3 - 3 ln ∣ x + 3 ∣ + C

Schritte zur Lösung

\int \frac{x}{x + 3} d x

Wende U-Substitution an

= \int \frac{u - 3}{u} d u

Multipliziere aus

\frac{u - 3}{u} : 1 - \frac{3}{u}

= \int 1 - \frac{3}{u} d u

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 u - \int \frac{3}{u} d u

\int 1 d u = u

\int \frac{3}{u} d u = 3 ln ∣ u ∣

= u - 3 ln ∣ u ∣

Setze in

u = x + 3

ein

= x + 3 - 3 ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= x + 3 - 3 ln ∣ x + 3 ∣ + C

\frac{\partial}{\partial y} (4 x^{2} y)

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

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

\int (3 x - 1) (x + 1) d x

\int \frac{sin ( 3 x )}{2 + cos ( 3 x )} d x